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Technical Report Documentation Page 1. Report No. FHWA/TX-05/0-4468-2
2. Government Accession No.
3. Recipient's Catalog No. 5. Report Date December 2004 Resubmitted: August 2005
4. Title and Subtitle COMPARISON OF FATIGUE ANALYSIS APPROACHES FOR TWO HOT MIX ASPHALT CONCRETE (HMAC) MIXTURES
6. Performing Organization Code
7. Author(s) Lubinda F. Walubita, Amy Epps Martin, Sung Hoon Jung, Charles J. Glover, Eun Sug Park, Arif Chowdhury, and Robert L. Lytton
8. Performing Organization Report No. Report 0-4468-2
10. Work Unit No. (TRAIS)
9. Performing Organization Name and Address Texas Transportation Institute The Texas A&M University System College Station, Texas 77843-3135
11. Contract or Grant No. Project 0-4468 13. Type of Report and Period Covered Technical Report: September 2002-August 2004
12. Sponsoring Agency Name and Address Texas Department of Transportation Research and Technology Implementation Office P. O. Box 5080 Austin, Texas 78763-5080
14. Sponsoring Agency Code
15. Supplementary Notes Project performed in cooperation with the Texas Department of Transportation and the Federal Highway Administration. Project Title: Evaluate the Fatigue Resistance of Rut Resistance Mixes URL: http://tti.tamu.edu/documents/0-4468-2.pdf 16. Abstract Over the past decade, the Texas Department of Transportation (TxDOT) focused research efforts on improving mixture design to preclude rutting in the early life of the pavement. However, these rut resistant stiff mixtures may be susceptible to long-term fatigue cracking in the pavement structure as the binder stiffens due to oxidative aging. To address this concern, TxDOT initiated a research study with the primary goal of evaluating and recommending a HMAC mixture fatigue design and analysis system to ensure adequate mixture fatigue performance in a particular pavement structure under specific environmental and traffic loading conditions. A secondary goal of the research was to compare the fatigue resistance of commonly used TxDOT HMAC mixtures including investigating the effects of binder aging on fatigue performance. Four fatigue analysis approaches, the mechanistic empirical (ME), the calibrated mechanistic with (CMSE) and without (CM) surface energy measurements, and the proposed NCHRP 1-37A Pavement Design Guide were investigated in this project to evaluate the fatigue resistance of two common TxDOT mixtures (Rut Resistant and Basic Type C) including the effects of aging. Based on the value engineering assessment including test results, statistical analysis, costs, and relative comparison of each analysis procedure, the continuum micromechanics based CMSE fatigue analysis approach was recommended for predicting HMAC mixture fatigue life (Nf). While binder oxidative aging reduced the HMAC mixture resistance to fracture and its ability to heal, the Rut Resistant mixture exhibited better fatigue resistance in terms of Nf magnitude compared to the Basic Type C mixture possibly due to an increased polymer modified binder content. Test results also indicated that both binders and mixtures stiffen with oxidative aging, and that mixture aging correlated quantitatively with binder aging. From the binder shear properties and binder-mixture relationships, aging shift factors were developed and produced promising results. Nonetheless, more CMSE laboratory HMAC mixture fatigue characterization and field validation is recommended. 17. Key Words Asphalt, Asphalt Concrete, Fatigue, Aging, Fracture, Microcracking, Healing, Mechanistic Empirical, Calibrated Mechanistic, Surface Energy, Anisotropy
18. Distribution Statement No restrictions. This document is available to the public through NTIS: National Technical Information Service Springfield, Virginia 22161 http://www.ntis.gov
19. Security Classif.(of this report) Unclassified
20. Security Classif.(of this page) Unclassified
21. No. of Pages 312
22. Price
Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
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COMPARISON OF FATIGUE ANALYSIS APPROACHES FOR TWO HOT MIX ASPHALT CONCRETE (HMAC) MIXTURES
by
Lubinda F. Walubita Graduate Research Assistant, Texas Transportation Institute
Amy Epps Martin
Associate Research Engineer, Texas Transportation Institute
Sung Hoon Jung Graduate Research Assistant, Texas Transportation Institute
Charles J. Glover
Research Engineer, Texas Transportation Institute
Eun Sug Park Assistant Research Scientist, Texas Transportation Institute
Arif Chowdhury
Associate Transportation Researcher, Texas Transportation Institute
and
Robert L. Lytton Research Engineer, Texas Transportation Institute
Report 0-4468-2 Project 0-4468
Project Title: Evaluate the Fatigue Resistance of Rut Resistance Mixes
Performed in cooperation with the Texas Department of Transportation
and the Federal Highway Administration
December 2004
Resubmitted: August 2005
TEXAS TRANSPORTATION INSTITUTE The Texas A&M University System College Station, Texas 77843-3135
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DISCLAIMER
The contents of this report reflect the views of the authors, who are responsible for the
facts and the accuracy of the data presented herein. The contents do not necessarily reflect the
official view or policies of the Federal Highway Administration (FHWA) or the Texas
Department of Transportation (TxDOT). This report does not constitute a standard,
specification, or regulation, nor it is intended for construction, bidding, or permit purposes.
Trade names were used solely for information and not for product endorsement. The engineers
in charge were Amy Epps Martin, P.E. (Texas No. 91053) and Charles J. Glover, P.E. (Texas
No. 48732).
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ACKNOWLEDGMENTS
This project was conducted for TxDOT, and the authors thank TxDOT and FHWA for
their support in funding this research project. In particular, the guidance and technical assistance
provided by the project director (PD) Gregory Cleveland of TxDOT, the project coordinator (PC)
James Travis of FHWA, and German Claros of the Research and Technology Implementation
(RTI) office is greatly appreciated. Special thanks are also due to Lee Gustavus, Rick Canatella,
Scott Hubley, Sharath Krishnamurthy, Amit Bhasin, Jeffrey Perry, and Andrew Fawcett from the
Texas Transportation Institute (TTI) and Texas Engineering Experiment Station (TEES) for their
help in specimen/sample preparation, laboratory testing, and data analysis. The various TxDOT
district offices that provided the material mix-designs and assistance in material procurement are
also thanked.
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TABLE OF CONTENTS
LIST OF FIGURES ..................................................................................................................... xiv
LIST OF TABLES....................................................................................................................... xix
CHAPTER 1. INTRODUCTION ....................................................................................................1
WORK PLAN............................................................................................................................1
SCOPE OF WORK....................................................................................................................3
DESCRIPTION OF CONTENTS..............................................................................................3
SUMMARY...............................................................................................................................4
CHAPTER 2. INFORMATION SEARCH......................................................................................5
FIELD SURVEY QUESTIONNARIES....................................................................................5
LITERATURE REVIEW ..........................................................................................................6
Prediction of HMAC Mixture Fatigue Resistance...............................................................6
Binder Aging and HMAC Mixture Fatigue Resistance.....................................................16
SELECTED FATIGUE ANALYSIS APPROACHES............................................................21
SUMMARY.............................................................................................................................22
CHAPTER 3. EXPERIMENTAL DESIGN..................................................................................23
HMAC MIXTURES AND MIX-DESIGN..............................................................................23
The Bryan (BRY) Mixture – Basic TxDOT Type C (PG 64-22 + Limestone) .................24
The Yoakum (YKM) Mixture – Rut Resistant 12.5 mm Superpave
(PG 76-22 + Gravel) ..........................................................................................................25
Material Properties for the Binders....................................................................................26
Material Properties for the Aggregates ..............................................................................28
HMAC SPECIMEN FABRICATION.....................................................................................29
Aggregate Batching ...........................................................................................................29
Mixing, Short Term Oven-aging, Compaction, and Air Voids .........................................31
Sawing, Coring, Handling, and Storage.............................................................................33
BINDER AND HMAC MIXTURE AGING CONDITIONS .................................................34
HYPOTHETICAL FIELD PAVEMENT STRUCTURES AND TRAFFIC ..........................35
ENVIRONMENTAL CONDITIONS .....................................................................................36
RELIABILITY LEVEL...........................................................................................................38
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TABLE OF CONTENTS (continued)
ELSYM5 STRESS-STRAIN ANALYSIS ..............................................................................39
ELSYM5 Input/Output Data..............................................................................................39
FEM Strain-Adjustment.....................................................................................................40
SUMMARY.............................................................................................................................41
CHAPTER 4. THE MECHANISTIC EMPIRICAL APPROACH ...............................................43
FUNDAMENTAL THEORY..................................................................................................43
INPUT/OUTPUT DATA.........................................................................................................45
LABORATORY TESTING.....................................................................................................46
The BB Fatigue Test Protocol............................................................................................46
Test Conditions and Specimens .........................................................................................48
Test Equipment and Data Measurement ............................................................................49
FAILURE CRITERIA ............................................................................................................50
ANALYSIS PROCEDURE.....................................................................................................50
Step 1. Laboratory Test Data Analysis (N-εt Empirical Relationship) ..............................51
Step 2. Stress-Strain Analysis, εt (Design) .............................................................................52
Step 3. Statistical Prediction of HMAC Mixture Fatigue Resistance, Nf(Supply) .................52
Step 4. Determination of the Required Pavement Fatigue Life, Nf(Demand).........................53
Step 5. Fatigue Design Check for Adequate Performance ................................................54
VARIABILITY, STATISTICAL ANALYSIS, AND Nf PREDICTION ................................54
SUMMARY.............................................................................................................................57
CHAPTER 5. THE CALIBRATED MECHANISTIC APPROACH WITH SURFACE
ENERGY………. ..........................................................................................................................59
FUNDAMENTAL THEORY AND DEVELOPMENT..........................................................59
INPUT/OUTPUT DATA.........................................................................................................62
LABORATORY TESTING.....................................................................................................65
Tensile Strength Test .........................................................................................................65
Relaxation Modulus Test ...................................................................................................66
Uniaxial Repeated Direct-Tension Test.............................................................................69
Anisotropic Test.................................................................................................................72
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TABLE OF CONTENTS (continued)
Surface Energy Measurements for the Binder – The Wilhelmy Plate Test .......................76
Surface Energy Measurements for the Aggregate – The Universal Sorption Device .......81
FAILURE CRITERIA ............................................................................................................87
ANALYSIS PROCEDURE.....................................................................................................87
Shift Factor Due to Anisotropic Effect, SFa ......................................................................88
Shift Factor Due to Healing Effect, SFh.............................................................................89
Other Shift Factors.............................................................................................................93
Number of Load Cycles to Crack Initiation, Ni .................................................................97
Number of Load Cycles to Crack Propagation, Np ..........................................................100
Surface Energies, ∆GhAB, ∆Gh
LW, and ∆Gf .......................................................................102
Relaxation Modulus, Ei, Exponent, mi, and Temperature Correction Factor, aT .............104
DPSE and Constant, b .....................................................................................................105
Crack Density, CD ............................................................................................................110
Shear Strain, γ ..................................................................................................................110
VARIABILITY, STATISTICAL ANALYSIS, AND Nf PREDICTION ..............................111
SUMMARY...........................................................................................................................112
CHAPTER 6. THE CALIBRATED MECHANISTIC APPROACH WITHOUT SURFACE
ENERGY .....................................................................................................................................115
LABORATORY TESTING...................................................................................................118
SE Measurements for Binders and Aggregates ...............................................................118
RM Test in Compression .................................................................................................118
ANALYSIS PROCEDURE...................................................................................................118
Shift Factor Due to Healing, SFh .....................................................................................119
Paris’ Law Fracture Parameters, A and n.........................................................................119
SUMMARY...........................................................................................................................120
CHAPTER 7. THE PROPOSED NCHRP 1-37A 2002 PAVEMENT DESIGN GUIDE...........123
FUNDAMENTAL THEORY................................................................................................123
INPUT/OUTPUT DATA.......................................................................................................125
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TABLE OF CONTENTS (continued)
LABORATORY TESTING...................................................................................................126
Dynamic Shear Rheometer Test ......................................................................................126
Dynamic Modulus Test....................................................................................................126
FAILURE CRITERIA ..........................................................................................................131
ANALYSIS PROCEDURE...................................................................................................131
VARIABILITY, STATISTICAL ANALYSIS, AND Nf PREDICTION..............................132
SUMMARY...........................................................................................................................132
CHAPTER 8. BINDER OXIDATIVE HARDENING BACKGROUND AND TESTING
METHODOLOGY ......................................................................................................................135
BINDER OXIDATION AND EMBRITTLEMENT (52, 93) ...............................................135
BINDERS STUDIED ............................................................................................................140
Laboratory-Aged Binders ................................................................................................140
Binders Recovered from HMAC Mixtures......................................................................140
BINDER TESTS....................................................................................................................141
Size Exclusion Chromatography .....................................................................................141
Dynamic Shear Rheometer .............................................................................................142
Ductility ...........................................................................................................................142
Fourier Transform Infrared Spectrometer (FTIR) ...........................................................143
SUMMARY...........................................................................................................................143
CHAPTER 9. BINDER-HMAC MIXTURE CHARACTERIZATION .....................................145
METHODOLOGY ................................................................................................................146
Binder Data Analysis .......................................................................................................147
HMAC Mixture Tests ......................................................................................................147
HMAC Mixture Visco-Elastic Characterization..............................................................149
RESULTS ..............................................................................................................................153
Recovered Binder Results................................................................................................154
HMAC Mixture Results...................................................................................................159
Binder-Mixture Comparisons ..........................................................................................164
SUMMARY...........................................................................................................................165
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TABLE OF CONTENTS (continued)
CHAPTER 10. HMAC MIXTURE RESULTS AND ANALYSIS ............................................167
MIXTURE PROPERTIES FOR PREDICTING Nf...............................................................167
BB Laboratory Test Results.............................................................................................167
Nf-εt Empirical Relationships...........................................................................................168
Tensile Strength (σt) ........................................................................................................170
Relaxation Modulus Master-Curves ................................................................................172
RM Temperature Shift Factors, aT...................................................................................174
Dissipated Pseudo Strain Energy (DPSE) and Fracture Damage ...................................176
Surface Energy.................................................................................................................177
Mixture Anisotropy..........................................................................................................179
Dynamic Modulus Results...............................................................................................180
HMAC MIXTURE FATIGUE LIVES (Nf)...........................................................................181
ME Lab Nf Results ...........................................................................................................181
CMSE Lab Nf Results ......................................................................................................182
CM Lab Nf Results...........................................................................................................183
Mixture Field Nf Results – ME, CMSE, and CM Analyses.............................................185
Mixture Field Nf Results – The M-E Pavement Design Guide Analysis.........................187
DEVELOPMENT OF CMSE SHIFT FACTORS DUE TO AGING ...................................188
Theoretical Basis and Assumptions .................................................................................188
SFag Formulation and the Binder DSR Master-Curves....................................................189
CMSE-CM Field Nf Prediction Using SFag......................................................................192
SUMMARY...........................................................................................................................193
BB Testing .......................................................................................................................193
Tensile Stress ...................................................................................................................193
Relaxation Modulus .........................................................................................................193
DPSE and SE Results.......................................................................................................194
Mixture Anisotropy..........................................................................................................194
Mixture Nf ........................................................................................................................195
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TABLE OF CONTENTS (continued)
CHAPTER 11. DISCUSSION AND SYNTHESIS OF RESULTS ............................................197
COMPARISON OF MIXTURE FIELD Nf ...........................................................................197
MIXTURE VARIABILITY...................................................................................................201
EFFECTS OF OTHER INPUT VARIABLES ON MIXTURE FIELD Nf ...........................203
Pavement Structure ..........................................................................................................203
Environmental Conditions ...............................................................................................205
BINDER TEST RESULTS AND EFFECTS OF AGING ....................................................206
BINDER-MIXTURE CHARACTERIZATION AND AN AGING SHIFT FACTOR ........212
SUMMARY...........................................................................................................................219
CHAPTER 12. COMPARISON AND SELECTION OF THE FATIGUE ANALYSIS
APPROACH ................................................................................................................................221
COMPARATIVE REVIEW OF THE FATIGUE ANALYSIS APPROACHES .................221
Theoretical Concepts .......................................................................................................223
Input Data.........................................................................................................................224
Laboratory Testing...........................................................................................................224
Failure Criteria .................................................................................................................225
Data Analysis ...................................................................................................................227
Results and Variability.....................................................................................................228
Costs - Time Requirements for Laboratory Testing and Data Analysis..........................229
Costs - Equipment............................................................................................................230
SELECTION OF FATIGUE ANALYSIS APPROACH ......................................................230
TxDOT Evaluation Survey Questionnaire.......................................................................232
Assessment and Rating Criteria of the Fatigue Analysis Approaches.............................234
The Selected Fatigue Analysis Approach – The CMSE Approach .................................235
Incorporation of Aging Effects in Field Nf Prediction ....................................................236
Recommendations on a Surrogate Fatigue Test and Analysis Protocol .........................236
SUMMARY ..........................................................................................................................237
CHAPTER 13. CONCLUSIONS, RECOMMENDATIONS, AND FUTURE WORK .............239
CONCLUSIONS....................................................................................................................239
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TABLE OF CONTENTS (continued)
Selected Fatigue Analysis Approach - CMSE.................................................................239
Comparison of Mixture Field Nf ......................................................................................241
Effects of Binder Oxidative Aging and Other Variables .................................................241
Binder-Mixture Characterization .....................................................................................242
RECOMMENDATIONS.......................................................................................................243
CLOSURE .............................................................................................................................244
CURRENT AND FUTURE FY05 WORK ...........................................................................244
REFERENCES ............................................................................................................................247
APPENDICES .............................................................................................................................263
APPENDIX A: EVALUATION FIELD SURVEY QUESTIONNAIRE
(FOR GOVERNMENT AGENCIES AND THE INDUSTRY)............................................265
APPENDIX B: HMAC ANISOTROPIC ADJUSTMENT FACTORS ...............................267
APPENDIX C: BENDING BEAM LABORATORY TEST DATA FOR THE
MECHANISTIC EMPIRICAL APPROACH .......................................................................269
APPENDIX D: DYNAMIC MODULUS LABORATORY TEST DATA FOR
THE M-E PAVEMENT DESIGN GUIDE ...........................................................................271
APPENDIX E: EXAMPLE OF PERCENTAGE CRACKING ANALYSIS FROM
THE M-E PAVEMENT DESIGN GUIDE SOFTWARE.....................................................273
APPENDIX F: ME MIXTURE LAB Nf RESULTS ............................................................275
APPENDIX G: CMSE MIXTURE LAB Nf RESULTS.......................................................277
APPENDIX H: CM MIXTURE LAB Nf RESULTS............................................................279
APPENDIX I: MIXTURE FIELD Nf RESULTS.................................................................281
APPENDIX J: RESOURCE REQUIREMENTS .................................................................287
APPENDIX K: TxDOT EVALUATION SURVEY QUESTIONNAIRE...........................289
APPENDIX L: RATING CRITERIA OF THE FATIGUE ANALYSIS APPROACHES..291
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LIST OF FIGURES
Figure Page
2-1 Master-Curve for SHRP AAB-1 at Two Aging Times (°F = 32 +1.8(°C)) .......................18
2-2 Effect of Aging on Low Shear-Rate Limiting Viscosity (°F = 32 +1.8(°C)) .....................18
2-3 Continuous Bottom Grade as a Function of PAV Aging Time (°F = 32 +1.8(°C)) ...........19
2-4 Ductility versus DSR Function G’/(η/G’) (°F = 32 +1.8(°C)) ...........................................20
3-1 Limestone Aggregate Gradation Curve for TxDOT Type C Mixture ...............................24
3-2 Gravel Aggregate Gradation Curve for Rut Resistant 12.5 mm Superpave Mixture.........25
3-3 Binder High Temperature Properties – G*/Sin δ, Pascal (°F = 32 +1.8(°C)),
(delta ≅ δ) ...........................................................................................................................26
3-4 Binder Low Temperature Properties - Flexural Creep Stiffness (MPa)
(°F = 32 +1.8(°C)) ..............................................................................................................27
3-5 Binder Low Temperature Properties (m-value) (°F = 32 +1.8(°C))...................................27
3-6 Superpave Gyratory Compactor .........................................................................................32
3-7 Linear kneading Compactor ...............................................................................................32
3-8 Laboratory Test Specimens (Drawing not to Scale) (1 mm ≅ 0.039 inches) .....................33
3-9 Fatigue Analysis Approaches and HMAC Mixture Aging Conditions
(°F = 32 +1.8(°C)) ..............................................................................................................35
3-10 Texas Environmental Zoning (60)......................................................................................37
4-1 The ME Fatigue Design and Analysis System ..................................................................44
4-2 The Bending Beam (BB) Device........................................................................................47
4-3 Loading Configuration for the BB Fatigue Test.................................................................47
4-4 Example of Temperature Plot for the BB Test ...................................................................49
4-5 Example of Stress Response from BB Testing at 20 °C (68 °F)
(374 microstrain level) .......................................................................................................50
5-1 Example of Hysteresis Loop (Shaded Area is DPSE)........................................................60
5-2 The CMSE Fatigue Design and Analysis System ..............................................................63
5-3 Loading Configuration for Tensile Strength Test...............................................................65
5-4 Loading Configuration for Relaxation Modulus Test ........................................................67
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LIST OF FIGURES (continued)
5-5 Example of Stress Response from RM Test at 10 °C (50 °F) ............................................68
5-6 Loading Configuration for the RDT Test...........................................................................70
5-7 Stress Response from RDT Testing at 30 °C (86 °F).........................................................71
5-8 Loading Configuration for the AN Test.............................................................................72
5-9 Example of Strain Responses from AN Testing at 20 °C (68 °F)......................................74
5-10 Loading Configuration for the Wilhelmy Plate Test Method ............................................76
5-11 The DCA Force Balance and Computer Setup – Wilhelmy Plate Test .............................78
5-12 Example of the DCA Software Display (Advancing and Receding) .................................79
5-13 USD Setup..........................................................................................................................82
5-14 Example of Adsorption of n-Hexane onto Limestone under USD Testing .......................84
5-15 Output Stress Shape Form from RDT Test ......................................................................108
5-16 Example of WR – Log N Plot ...........................................................................................109
5-17 Brittle Crack Failure Mode (Marek and Herrin [88]).......................................................110
6-1 The CM Fatigue Design and Analysis System.................................................................116
7-1 The Fatigue Design and Analysis System for the M-E Pavement Design guide as
Utilized in this Project......................................................................................................124
7-2 Loading Configuration for Dynamic Modulus Test.........................................................127
7-3 The Universal Testing Machine .......................................................................................128
7-4 Compressive Axial Strain Response from DM Testing at 4.4 °C (40 °F) .......................129
8-1 The Maxwell Model .........................................................................................................136
8-2 Correlation of Aged-Binder Ductility with the DSR Function G’/(η’/G’) for
Unmodified Binders (52) (°F = 32 + 1.8(°C)) .................................................................137
8-3 Binder Aging Path on a G’ vs. η’/G’ Map (Pavement-aged Binders) (52)
(°F = 32 + 1.8(°C)). ..........................................................................................................138
9-1 Binder Oxidative Aging and Testing (°F = 32 + 1.8(°C))................................................146
9-2 Binder-Mixture Characterization Test Procedure (°F = 32 + 1.8(°C)).............................148
9-3 Relaxation Master-Curve for 0 Month Aged Yoakum Mixture Used for CMSE
(°F = 32 + 1.8(°C)) .........................................................................................................149
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LIST OF FIGURES (continued)
9-4 Shear Modulus Master-Curve for 0 Month Aged Yoakum Mixture Used for CMSE
(°F = 32 + 1.8(°C)) ...........................................................................................................153
9-5 Master-Curves of Recovered Binders for G*(ω) from Bryan Mixture
(°F = 32 + 1.8(°C)) .......................................................................................................155
9-6 Master-Curves of Recovered Binders for G*(ω) from Yoakum Mixture
(°F = 32 + 1.8(°C)) .......................................................................................................155
9-7 Master-Curve of Recovered Binders for G’(ω), G”(ω) from Bryan Mixture
(°F = 32 + 1.8(°C)) .......................................................................................................156
9-8 Master-Curve of Recovered Binders for G’(ω), G”(ω) from Yoakum Mixture
(°F = 32 + 1.8(°C)) .......................................................................................................156
9-9 DSR Function of Recovered Binders from Bryan Mixture (°F = 32 + 1.8(°C)) ..............157
9-10 DSR Function of Recovered Binders from Yoakum Mixture (°F = 32 + 1.8(°C)) ..........158
9-11 Master-Curves of Bryan Mixture for E(t) (°F = 32 + 1.8(°C)).........................................159
9-12 Master-Curves of Yoakum Mixtures for E(t) (°F = 32 + 1.8(°C)) ...................................160
9-13 Master-Curves of Bryan Mixture for G’(ω), G”(ω) (°F = 32 + 1.8(°C)).........................161
9-14 Master-Curves of Yoakum Mixture for G’(ω), G”(ω) (°F = 32 + 1.8(°C)).....................162
9-15 Master-Curve Comparisons between Bryan and Yoakum Mixtures for G*(ω)
(°F = 32 + 1.8(°C)) ...........................................................................................................162
9-16 VE Function of Bryan Mixture (°F = 32 + 1.8(°C)).........................................................163
9-17 VE Function of Yoakum Mixture (°F = 32 + 1.8(°C)).....................................................164
9-18 VE Function vs. DSR Function (°F = 32 + 1.8(°C)) ........................................................165
10-1(a) N vs. εt at 20 °C (68 °F) (Bryan Mixture) ......................................................................169
10-1(b) N vs. εt at 20 °C (68 °F) (Yoakum Mixture)..................................................................169
10-2(a) Mixture Tensile Stress at 20 °C (68 °F) (Bryan Mixture)...............................................171
10-2(b) Mixture Tensile Stress at 20 °C (68 °F) (Yoakum Mixture) ..........................................171
10-2(c) Failure Tensile Strain (εf) at Break at 20 °C (68 °F).......................................................172
10-3(a) RM (Tension) Master-Curve at 20 °C (68 °F) (Bryan Mixture).....................................173
10-3(b) RM (Tension) Master-Curve at 20 °C (68 °F) (Yoakum Mixture).................................173
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LIST OF FIGURES (continued)
10-4(a) Temperature Shift Factors, aT Tref = 20 °C (Bryan Mixture) (°F = 32 + 1.8(°C))...............175
10-4(b) Temperature Shift Factors, aT at Tref = 20 °C (Yoakum Mixture) (°F = 32 + 1.8(°C)).......175
10-5 Mixture DPSE at 20 °C (68 °F): Constant b vs. Aging Condition .................................176
10-6(a) Mixture Fracture Energy (∆Gf), ergs/cm2 (adhesive, dry-conditions) . .........................177
10-6(b) Mixture Healing Energy (∆Gh), ergs/cm2 (adhesive, dry-conditions) ............................178
10-7 Mixture Lab Nf at 20 °C (68 °F) for PS#1, WW Environment
(Bryan vs. Yoakum Mixture) – ME Analysis.................................................................182
10-8 Mixture Lab Nf at 20 °C (68 °F) for PS#1, WW Environment
(Bryan vs. Yoakum Mixture) – CMSE Analysis ..........................................................183
10-9 Mixture Lab Nf at 20 °C (68 °F) for PS#1, WW Environment
(Bryan vs. Yoakum Mixture) – CM Analysis...............................................................184
10-10(a) Field Nf for PS#1, WW Environment – ME Analysis...................................................185
10-10(b) Field Nf for PS#1, WW Environment – CMSE Analysis .............................................186
10-10(c) Field Nf for PS#1, WW Environment – CM Analysis ..................................................186
10-11 Field Nf for PS#1, WW Environment – M-E Design Guide Analysis. ........................187
10-12 Binder DSRf (ω) Master-Curves @ 20 °C (68 °F) .........................................................191
11-1(a) Mixture Field Nf (0 Months, PS#1, WW Environment) ................................................197
11-1(b) Mixture Field Nf (3 Months, PS#1, WW Environment)................................................198
11-1(c) Mixture Field Nf (6 Months, PS#1, WW Environment)................................................198
11-1(d) Mixture Field Nf Comparison (PS#1, WW Environment) ............................................199
11-2 Effect of Pavement Structure on Mixture Field Nf
(Bryan Mixture, WW Environment)..............................................................................204
11-3 Effect of Environmental Conditions on Mixture Field Nf (PS#1).................................205
11-4 SEC Chromatogram for Recovered Binders from Bryan Mixtures
(°F = 32 + 1.8 (°C)) ..........................................................................................................207
11-5 CA Rate of Bryan Binder (PG 64-22) (°F = 32 + 1.8 (°C)) ..........................................208
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LIST OF FIGURES (continued)
11-6 Zero Shear Viscosity Hardening Rate of Bryan Binder (PG 64-22)
(°F = 32 + 1.8 (°C)) ..........................................................................................................208
11-7 DSR Function vs. Carbonyl Area of Bryan Binder (PG 64-22) (°F = 32 + 1.8(°C)) ....209
11-8 DSR Function Hardening Rate of Yoakum Binder (PG 76-22) (°F = 32 + 1.8(°C)) ....210
11-9 CA Rate of Yoakum Binder (PG 76-22) (°F = 32 + 1.8(°C)) .......................................211
11-10 DSR Function vs. CA of Yoakum Binder (PG 76-22) (°F = 32 + 1.8(°C)) ..................212
11-11 Decline of Field Nf with Binder DSR Function Hardening (°F = 32 + 1.8(°C))...........214
11-12 DSR Function Hardening Rate of Neat Binder after Initial Jump
(°F = 32 + 1.8 (°C)) ..........................................................................................................215
11-13 Calculated Decline of Remaining Pavement Fatigue Service Life ...............................216
11-14 Hypothetical Decline of Pavement Fatigue Service life, Initial Fatigues Equal ..........217
11-15 Hypothetical Decline of Pavement Fatigue Service life, Ki Values Equal...................219
12-1 Assessment Factors/Sub-factors and Associated Weighting Scores ............................233
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LIST OF TABLES
Table Page
3-1 Intermediate Temperature Properties of the Binders at 25 °C (77 °F)...............................28
3-2 Aggregate Properties ..........................................................................................................29
3-3 Limestone Aggregate Gradation for TxDOT Type C Mixture ..........................................30
3-4 Gravel Aggregate Gradation for 12.5 mm Superpave Mixture..........................................30
3-5 HMAC Mixture Mixing and Compaction Temperatures...................................................31
3-6 Aging Conditions for Binders and HMAC Compacted Specimens...................................34
3-7 Selected Pavement Structures and Traffic .........................................................................36
3-8 Computed Critical Design Strains......................................................................................41
4-1 Summary of ME Fatigue Analysis Input and Output Data ...............................................46
5-1 Summary of CMSE Fatigue Analysis Input and Output Data...........................................64
5-2 Surface Energy Components of Water, Formamide, and Glycerol...................................78
5-3 Surface Energy Components of Water, n-hexane, and MPK............................................83
5-4 Fatigue Calibration Constants Based on Backcalculation of Asphalt Moduli from FWD
Tests (Lytton et al. [45]) ...................................................................................................92
5-5 Fatigue Calibration Constants based on Laboratory Accelerated Tests
(Lytton et al. [45]) ..............................................................................................................92
6-1 Summary of CM Fatigue Analysis Input and Output Data .............................................117
7-1 Analysis Input/Output Data for the M-E Pavement Design Guide Software..................125
7-2 Example of Output Data from DM Testing at 4.4 °C (40 °F) .........................................130
10-1 BB Laboratory Test Results ............................................................................................167
10-2 Mixture Empirical Fatigue Relationships........................................................................168
10-3 Mixture Tensile Strength .................................................................................................170
10-4 Mixture Relaxation Modulus (Tension) Test Data..........................................................172
10-5 Paris’ Law Fracture Coefficient A and SFh Values .........................................................178
10-6 Mixture Anisotropic Results............................................................................................180
10-7 CM vs. CMSE Mixture Lab Nf Results for PS#1, WW Environment.............................184
10-8 CMSE-CM SFag Values...................................................................................................190
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LIST OF TABLES (Continued)
10-9 Example of Field Nf Predictions at Year 20 (PS#1, WW Environment).........................192
11-1 Example of HMAC Specimen AV Variability................................................................201
11-2 Example of Mixture Field Nf Variability (PS# 1, WW Environment) ............................202
11-3 Summary of Pavement Fatigue Life Parameters .............................................................215
12-1(a) Summary Comparison of the Fatigue Analysis Approaches ..........................................221
12-1(b) Summary Comparison of the Fatigue Analysis Approaches ..........................................222
12-1(c) Summary Comparison of the Fatigue Analysis Approaches ..........................................223
12-1(d) Summary Comparison of the Fatigue Analysis Approaches ..........................................223
12-2 Summary Comparison of Figure Analysis Approaches .................................................231
12-3 Weighted Scores and Rating of the Fatigue Analysis Approaches ................................234
13-1 Example of a Factorial Experimental Design for FY05.................................................245
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CHAPTER 1 INTRODUCTION
Hot mix asphalt concrete (HMAC) mixtures are designed to resist aging and
distress induced by traffic loading and changing environmental conditions. Common
HMAC distresses include rutting, fatigue, and thermal cracking. Over the past decade, the
Texas Department of Transportation (TxDOT) focused research efforts on improving
mixture design to preclude rutting in the early life of the pavement. Improvements in
rutting resistance also offered increased resistance to moisture damage. However, a
concern arose that these stiff mixtures may be susceptible to fatigue cracking in the long
term in the pavement structure, particularly if the binder stiffens excessively due to
oxidative aging. Therefore, in 2002 TxDOT initiated a research study with the following
two primary objectives:
(1) To evaluate and recommend a fatigue HMAC mixture design and analysis system
for TxDOT to ensure adequate mixture performance in a particular pavement
structure under specific environmental and traffic loading conditions that
incorporates the effects of binder oxidative aging.
(2) To comparatively evaluate and establish a database of fatigue resistance of
commonly used TxDOT HMAC mixtures.
WORK PLAN
To accomplish these goals, researchers utilized four fatigue analysis approaches
to predict fatigue lives of one common TxDOT mixture and another TxDOT mixture
frequently used for rutting resistance under representative environmental conditions and
typical loading conditions in standard pavement structures.
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The selected approaches included the following:
• the mechanistic empirical (ME) approach developed during the Strategic Highway
Research Program (SHRP) using the bending beam fatigue test (1,2);
• the proposed National Cooperative Highway Research Program (NCHRP) 1-37A
2002 Pavement Design Guide using the dynamic modulus test (3, 4);
• a calibrated mechanistic (CM) approach developed at Texas A&M University that
requires strength and repeated loading tests in uniaxial tension and relaxation tests in
uniaxial tension and compression for material characterization and monitoring
dissipated pseudo strain energy (5); and
• an updated calibrated mechanistic (CMSE) approach developed at Texas A&M
University that also requires measuring surface energies of component materials in
addition to the material characterization tests from the original calibrated mechanistic
approach (6).
At the conclusion of the original project in August 2004, the research team
recommended the best approach for fatigue design and analysis based on a value
engineering assessment. This comparison of the four fatigue analysis approaches
considered variability; required resources; implementation issues; the ability to
incorporate the important effects of aging, fracture, and healing; practicality; and the
capability to interface with pavement design. A key element of this two-year research
effort was progress made in the investigation of the relationship between the change in
mixture fatigue resistance due to aging and aged binder properties. With a better
understanding of this relationship, the effects of aging on fatigue life may be quantified.
In a modified third year of the project, fatigue lives of additional mixtures will be
predicted using the recommended CMSE design and analysis system. These additional
mixtures will explore the effects on fatigue life of mixture parameters, including binder
content and binder or modifier type. Further investigation of the effects of aging on
mixture fatigue resistance is also being pursued.
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SCOPE OF WORK
This interim report documents the following:
(1) detailed descriptions of the four fatigue analysis approaches used to predict fatigue
life,
(2) a comparison of fatigue lives of two TxDOT HMAC mixtures,
(3) the effect of binder oxidative aging on binder and mixture properties and fatigue
resistance,
(4) binder-mixture relationships with respect to binder oxidative aging, and
(5) development of shift factors due to aging based on binder visco-elastic properties.
The report describes fatigue analysis results for the two selected mixtures in five
specific pavement structures designed over a range of typical traffic loading conditions
and under two representative Texas environmental conditions.
DESCRIPTION OF CONTENTS
The interim report is divided into 13 chapters including this chapter (Chapter 1)
that provides the motivation for the project, the overall objectives and work plan, and the
scope of this report. The subsequent chapters describe the information search (Chapter 2)
and experimental design (Chapter 3) that includes selection of fatigue analysis
approaches, materials, specimen fabrication protocols, aging conditions, and typical
pavement structures. Next, the four fatigue analysis approaches are described in detail in
Chapters 4 through 7. Chapter 8 describes binder testing followed by the testing and
analysis utilized to explore the relationship between binder and HMAC mixture aging in
Chapter 9. Then, the results, including the resulting fatigue lives from all the approaches
and the aging evaluation, are described and discussed in Chapters 10, 11, and 12. This
report concludes in Chapter 13 with a summary of findings, recommendations, and a
work plan to complete the project in a modified third year. Appendices of detailed
laboratory test results and other important data are also included.
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SUMMARY
The following bullets summarize the project objectives, the work plan, scope of
work, and the contents of this interim report:
• The primary objectives of this project were twofold:
(1) to evaluate and recommend a fatigue HMAC mixture design and analysis system
for TxDOT to ensure adequate mixture performance in a particular pavement
structure under specific environmental and traffic loading conditions that
incorporates the effects of binder oxidative aging, and
(2) to comparatively evaluate and establish a database of fatigue resistance of
commonly used TxDOT HMAC mixtures.
• The work plan entailed utilization of four fatigue analysis approaches (mechanistic
empirical and calibrated mechanistic) to predict fatigue lives of one common TxDOT
mixture and another TxDOT mixture frequently used for rutting resistance under
representative environmental conditions and typical loading conditions in standard
pavement structures. Thereafter, the best approach for fatigue design and analysis
was recommended based on a value engineering assessment including the ability to
incorporate practicality and the important effects of aging, fracture, and healing.
• The scope of the research work was limited to: a) two TxDOT HMAC mixtures,
b) four fatigue analysis approaches, c) three binder oxidative aging conditions, d) five
standard pavement structures, and e) two Texas environmental conditions.
• The report consists of 13 chapters. Chapter 1 is the introduction, and Chapters 2 and 3
are the information search and experimental design, respectively. Chapters 4 through
7 describe the four fatigue analysis approaches, followed by binder testing in Chapter
8. Chapter 9 describes the binder-mixture characterization with respect to aging.
Mixture results are presented in Chapter 10, followed by a discussion, conclusions,
recommendations, and future work plans in Chapters 11, 12, and 13. Other data
including detailed laboratory test results are included in the appendices.
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CHAPTER 2
INFORMATION SEARCH
An information search utilizing a field survey questionnaire, electronic databases, and
resulting publications was conducted to gather data on current fatigue design and analysis
approaches; related laboratory tests, materials, pavement structures and design; corresponding
standards or references; and resources or methodologies used to obtain fatigue resistant HMAC
mixtures. Effects of aging, healing, and fracture on fatigue HMAC mixture performance were
also reviewed; and the literature found was summarized and documented. Researchers also
reviewed and documented commonly used TxDOT mixtures, material characteristics, and other
general input parameters including pavement structures, traffic loading, environmental
conditions, mix designs, aging conditions, and reliability levels.
Data gathered from the information search aided the research team in selecting the
appropriate fatigue analysis approaches for a comparative evaluation and subsequent
recommendation to TxDOT. These data also served as the basis for formulating the
experimental design including materials selection for this project.
FIELD SURVEY QUESTIONNAIRES
A field survey of government agencies and the industry addressed some of the
key aspects of fatigue analysis approaches, laboratory tests, material characteristics, pavement
structures and design, corresponding standards or references, and resources used for fatigue
resistant HMAC mixtures. Appendix A shows an example of the field survey questionnaire.
Thirty-nine surveys were emailed to a list of contacts familiar to the research team in the
industry, academia, and relevant personnel at state Departments of Transportation (DOTs).
Approximately half (10) of the 23 responses received do not consider fatigue in their HMAC
mixture design and analysis. Some of the responses referred the survey to other contacts, and
seven responses, primarily from research agencies, provided valuable references and information
that were reviewed and provided an input into the research methodology and experimental
design for the project. The results from these field survey questionnaires are summarized in
Appendix A from six respondents.
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Of the positive responses received, a majority of the DOTs and private industry use the
Superpave, mechanistic empirical, association of American State Highway and Transportation
Officials (AASHTO), Asphalt Institute, and visco-elastic continuum-damage analysis either for
mixture design and analysis or just to check for fatigue resistance in the final pavement structural
design (Appendix A). Laboratory tests include bending beam, dynamic modulus, indirect
tension, uniaxial fatigue, moisture sensitivity, and retained indirect tensile strength. Some of
these approaches and associated laboratory tests have been included in the experimental design
and are discussed subsequently.
LITERATURE REVIEW
From a detailed review of the information search, the research team summarized
information on the prediction of HMAC mixture fatigue resistance and binder aging and its
effects on HMAC mixture fatigue resistance.
Prediction of HMAC Mixture Fatigue Resistance
An approach that predicts HMAC mixture resistance to fatigue requires an understanding
and description of material behavior under repeated loads that simulate field conditions (1). This
broad description is valid for approaches that are mechanistic empirical to varying degrees. A
more empirically based approach requires that the laboratory test simulate field conditions, but a
constitutive law for material behavior in a more mechanics-based approach requires only
material properties determined from laboratory test(s) measured using a simple stress state if
possible.
In a review of flexure, supported flexure, direct uniaxial, diametral or indirect tension,
triaxial, fracture mechanics, and wheel-tracking test methods conducted a decade ago, continued
research in the use of dissipated energy and fracture mechanics approaches with flexure or direct
or indirect tension testing were recommended (1). This recommendation highlighted the shift
from more empirically based approaches to those able to incorporate a more fundamental
mechanistic understanding of fatigue crack initiation, crack propagation, and failure.
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This shift over the last decade toward the use of more applicable material behavior
models and numerical analysis methods to simulate the fatigue mechanism and failure was
possible due to the rapid increase in computing power. This section provides a brief review of
previous and current approaches that are more empirical in nature, those that provided a bridge
toward mechanistic analysis methods, and current mechanistic analysis approaches.
Mechanistic Empirical Approaches
Most previous approaches for predicting fatigue resistance of HMAC involve either
controlled stress or controlled strain laboratory testing at a single representative temperature over
a series of stress or strain levels, respectively, and determination of fatigue life at a stress or
strain level assumed to be critical and caused by a single type of vehicle load. These approaches
predict the number of stress or strain cycles to crack initiation in flexure, direct or indirect
tension, or semi-circular bending tests. A method to determine a single representative
temperature for laboratory testing and a temperature conversion factor to account for the fact that
loading occurs over a range in temperatures is required. A shift factor is also required to account
for other differences between field and laboratory conditions, including the effects of wander,
healing, and crack propagation. A lengthy testing program is required with replicate tests (to
account for relatively large variability) at different stress or strain levels to define an empirical
fatigue relationship for a specific HMAC mixture. The determination of the critical stress or
strain constitutes the mechanistic part of this type of approach, and this calculated value varies
depending on the assumed model of material behavior (where layered elastic is most commonly
used). The location of the critical stress or strain also limits the analysis to either bottom-up or
top-down fatigue cracking without consideration of both.
Even with the limitations of mechanistic-empirical approaches, validation has been
illustrated through comparisons with fatigue life measured in the field, particularly at accelerated
pavement testing (APT) facilities. The mechanistic empirical approach developed at the
University of California at Berkeley during the Strategic Highway Research Program as part of
Project A-003A provides a widely used example with results validated with full-scale Heavy
Vehicle Simulator (HVS) tests (2, 7, 8).
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Another mechanistic empirical approach explored at the University of Nottingham in
conjunction with the SHRP A-003A project was validated using a laboratory scale APT device.
Indirect tensile fatigue testing was also utilized at the University of Nottingham, and this testing
method was included in a comprehensive APT project that included scaled testing with the
Model Mobile Load Simulator (MMLS3). These approaches are described in brief detail in
subsequent subsections, followed by a subsection on improvements in mechanistic-empirical
approaches to account for changing environmental and loading conditions.
SHRP A-003A (University of California at Berkeley). The SHRP A-003A approach
utilizes the flexural beam fatigue test (third-point loading); incorporates reliability concepts that
account for uncertainty in laboratory testing, construction, and traffic prediction; and considers
environmental factors, traffic loading, and pavement design (2). Specimen preparation by rolling
wheel compaction is strongly recommended as part of this approach to simulate the engineering
properties of extracted pavement cores. Conditioning prior to testing to a representative or
worst-case aging state is also suggested. This approach was selected for this project as the
mechanistic empirical approach discussed in more detail in Chapter 4.
University of Nottingham. Fatigue research at the University of Nottingham provided
validation of the SHRP A-003A analysis system through wheel tracking tests and trapezoidal
fatigue testing (2, 9). Validation of flexural beam fatigue tests for one aggregate type was
successful for the thick wheel tracking slabs that approximated a controlled stress mode of
loading. Mixture rankings by the laboratory scale APT device were also approximately
equivalent to those based on indirect tensile stiffness and fatigue life determined by an indicator
of the ability to dissipate energy. Large variability in the wheel tracking results was highlighted.
Fatigue analysis continued at the University of Nottingham with the inclusion of a
visco-elastic model for material behavior that utilizes improvements in the conversion of
dynamic shear test results to dynamic flexural results first developed as part of the
SHRP A-003A system (2, 10).
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A visco-elastic material model was used in a mechanistic-empirical fatigue relationship
to predict crack initiation based on dissipated energy to account for nonsymmetrical stress/strain
response measured under full-scale loads and remove the effect of mode of loading during
laboratory testing. This model provides dissipated energy contour maps where the maximum
value can be located throughout the HMAC layer.
Indirect Tension Testing. Indirect tension offers a simple mode for dynamic
frequency sweep, fatigue, or strength testing, although a biaxial stress state and the inability to
test with stress reversal have been cited as disadvantages (11). The University of Nottingham
has utilized this testing mode in measuring stiffness and evaluating the fatigue resistance of
HMAC mixtures for overlay design (10).
More extensive indirect tensile fatigue testing for a range of materials in a complex
layered pavement structure was included in a comprehensive evaluation of two rehabilitation
strategies by TxDOT (12, 13). Relative fatigue lives were defined as the ratio of fatigue
resistance of untrafficked materials in these structures compared with those of the same materials
trafficked with a scaled APT device (MMLS3). These ratios provided an indication of the
detrimental effect of moisture damage and the improvement in fatigue resistance due to
increased temperatures and subsequent compaction. A series of time-consuming tests with an
average duration of 20 hours was completed at a single representative temperature
(20 °C [68 °F]) and frequency (10 Hz) with no rest periods in a controlled stress mode at a stress
level equal to 20 percent of the indirect tensile strength of the same HMAC material.
Tensile strength tests were also conducted in a semi-circular bending mode that induces a
direct tensile load to the center zone of a semi-circular shaped specimen to supplement the
indirect tensile test results. This test was considered as a possible candidate for fatigue testing in
this project due to reduced load requirements for the same stress level as compared to indirect
tensile testing, but it was not selected for evaluation because the associated analysis system is
still under development (14).
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Improvements to Mechanistic Empirical Approaches
The approach first developed during SHRP A-003A has been expanded further using the
full-scale APT WesTrack project to develop fatigue models and associated pay factors based on
construction quality (15, 16). The models developed were used to predict fatigue crack initiation
in the 26 original WesTrack sections.
Hourly changes in both environmental and traffic conditions (wander) were incorporated
in this mechanistic empirical analysis that assumed: (1) a critical binormal strain distribution
beneath dual tires at the base of the HMAC surface layer, (2) layered elastic behavior, and (3)
valid extrapolation of fatigue life for temperatures greater than 30 °C (86 °F). No shift factor
was applied to the fatigue life relationship that must be defined through laboratory testing for
each HMAC mixture type that is different from the Superpave WesTrack HMAC mixtures.
Empirical fatigue relationships developed by the Asphalt Institute and Shell have also
been improved through the definition of a continuous function of cumulative fatigue damage
using Miner’s Law to replace prediction of a specific level of fatigue cracking (17, 18). This
function assumes bottom-up cracking and utilizes a layered elastic material behavior model but
accounts for changing environmental and loading conditions in the accumulation of fatigue
damage. Further refinement with an expanded Long Term Pavement Performance (LTPP)
dataset that contains pavements exhibiting fatigue failure was recommended.
Tsai et al. have also adopted the Recursive Miner’s Law for cumulative fatigue damage
analysis of HMAC mixtures (18, 19). This Recursive Miner’s Law approach attempts to directly
incorporate the significant effects of traffic, environment, material properties, and pavement
structure in HMAC mixture fatigue modeling using mechanistic empirical relationships and a
Weibull-type fatigue life deterioration function. In their findings, Tsai et al. observed that
mixture properties played the most significant role in the fatigue damage accumulation of
HMAC pavement structures under traffic loading, while the randomness of vehicle speed and
traffic wander had the least effect (18).
Other research to further improve mechanistic empirical fatigue analysis has accounted
for the effects of dynamic loads (20). This approach considers a moving and fluctuating
concentrated load and utilizes Miner’s Law (19) with the assumption of bottom-up cracking to
predict fatigue crack initiation and cumulative fatigue damage.
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The Proposed NCHRP 1-37A 2002 Pavement Design Guide Methodology for Fatigue Resistance
The NCHRP 1-37A 2002 Pavement Design Guide adopts a mechanistic empirical
approach for the structural design of HMAC pavements (3). The basic inputs for pavement
design include environmental, materials, and traffic data. There are two major aspects of ME-
based material characterization: pavement response properties and major distress/transfer
functions (4).
Pavement response properties are required to predict states of stress, strain, and
displacement within the pavement structure when subjected to external wheel loads. These
properties for assumed elastic material behavior are the elastic modulus and Poisson’s ratio. The
major distress/transfer functions for asphalt pavements are load related fatigue fracture,
permanent deformation, and thermal cracking.
The current version of the NCHRP 1-37A 2002 Pavement Design Guide (and its
software), which is discussed in greater detail in Chapter 7, utilizes the Asphalt Institute damage
predictive equation (21). Unlike most ME-based approaches, this procedure incorporates two
types of fatigue damage criteria. Bottom-up fatigue cracking assumes crack initiation at the
bottom of the asphalt layer and propagation through the HMAC layer thickness to the surface.
Top-down fatigue cracking assumes crack initiation at the pavement surface and propagation
downward through the HMAC layer. In both failure criteria, tensile strain is the primary
mechanistic failure load-response parameter associated with crack growth. As discussed in
Chapter 7, this new design guide characterizes pavement materials in a hierarchical system
comprised of three input levels. Level 1 represents a design philosophy of the highest practically
achievable reliability, and Levels 2 and 3 have successively lower reliability.
For the 2002 Pavement Design Guide approach, NCHRP Project 9-19 researchers
suggested constructing a dynamic modulus master-curve for all HMAC mixtures. This master-
curve is developed by conducting frequency sweeps at five different temperatures and six
frequencies. The same master-curve can be used as an input for predicting rutting damage.
Preliminary efforts in NCHRP Project 9-19 did not show a strong correlation between dynamic
modulus and fatigue cracking at full-scale APT facilities (22). This finding provided increased
motivation to explore other approaches in this project.
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Toward Mechanistic Analysis
The shift toward mechanistic analysis of fatigue cracking was recognized and encouraged
through a review of the use of fracture mechanics in both HMAC and Portland cement concrete
(PCC) pavements (23). This history highlighted early efforts utilizing linear elastic fracture
mechanics and a single material property (K1c) providing the driving force for crack propagation
characterized by Paris’ Law.
Further efforts to consider a process zone ahead of the crack tip were also reviewed, and
the concept of similitude to provide a dimensionless parameter equivalent for both field and
laboratory conditions was described. A warning considering the specimen-size effect and its
implications for scaling cracking behavior was also issued.
The application of fracture mechanics to composite materials to advance the
understanding of the mechanism of fatigue cracking was recognized as a slow process but one
worth pursuing. This pursuit has continued to address the limitations of previous ME approaches
and expand the knowledge base and application of HMAC fatigue analysis.
Laboratory Test Programs. To address the limitation of a lengthy testing program,
researchers suggested characterizing the stiffness of HMAC using a master-curve from simple
dynamic direct or indirect tensile tests that reflects the dependence on time of loading and
temperature (24). Parameters from the master-curve were successfully used to predict the
coefficients in empirical fatigue relationships. The range of HMAC mixture variables, including
modified binders utilized in developing the regression relationships, were also provided.
Linear Visco-Elastic Models. To address the limitation of assumed layered elastic
material behavior, other researchers produced an integrated HMAC mixture and pavement
design that allows for more realistic linear visco-elastic behavior (25). This type of material
model accounts for asymmetrical stress-strain distributions under moving wheel loads and the
effect of time of loading history. In a multi-tiered analysis, the approach separately utilized two
conventional empirical fatigue relationships (based on strain and dissipated energy) for crack
initiation and Paris’ Law for crack propagation as described by Schapery (26).
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Laboratory testing requirements include frequency sweep, creep, and strength testing in
direct tension or compression at relevant temperatures. A nonlinear finite element simulation of
a multi-layer pavement structure that selects an appropriate HMAC stiffness as a function of a
more realistic asymmetrical stress state was also utilized in conjunction with mechanistic
empirical fatigue relationships (27). Numerical techniques were also used to model the behavior
of three specific materials using elastic-plastic fracture mechanics (28). Both crack initiation and
propagation were modeled, but the viscous behavior of HMAC was not taken into account.
Fracture Mechanics Approach. Further research toward improving the linear elastic
fracture mechanics approach with Paris’ Law as described by Schapery related the fracture
coefficients A and n and described the use of uniaxial dynamic and strength tests to determine
both parameters from a master stiffness curve and mixture correction factors (29). Crack
propagation using Paris’ Law was also incorporated successfully in two- and three-dimensional
finite element simulations (30). This approach spread complex simulation computations over the
material lifetime, incorporating damage and resulting stress redistribution. Crack propagation
was extrapolated between simulations to determine fatigue life from propagation of an initial
crack size assumed related to maximum aggregate size. This approach that assumes elastic
material response to a single type of load was validated using flexural beam fatigue tests.
Nonlinear fracture mechanics were applied to compare crack propagation parameters of different
materials at low temperatures and highlight the need to include effects of inelastic dissipated
energy in fatigue analysis (31).
Continuum Mechanics Approach. Research in fatigue analysis over the past decade has
expanded to include investigation of both damage due to repeated loading and healing due to
repeated rest periods (32, 33). Recovery of a loss in stiffness monitored during fatigue testing
was noted for short rest periods in direct uniaxial testing in a review of laboratory fatigue tests,
and the lack of fatigue cracking in thick HMAC pavements was attributed to a healing effect in
an evaluation toward revising design procedures (11, 34).
A continuum mechanics approach developed through research efforts at North Carolina
State University and Texas A&M University successfully accounted for damage growth through
crack initiation and propagation and healing for any load history or mode of loading (32, 33).
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This approach utilizes the visco-elastic correspondence principle and work potential
theory described by Schapery (26) to remove viscous effects in monitoring changes in pseudo-
stiffness in repeated uniaxial tensile tests. Coefficients in the visco-elastic constitutive model
describe differences in damage and healing behavior of different materials. This model was
validated with both laboratory and field results and behavior predicted from the micromechanical
approach also developed at Texas A&M University and described in a subsequent subsection
(33).
The continuum approach has also led to the development of two simplified fatigue
analysis systems (35, 36). One system predicts fatigue behavior for temperatures less than 20 °C
(68 °F) from a characteristic damage curve generated based on frequency sweep and strength
tests in uniaxial tension at multiple temperatures (35). Improvements to this system to consider
aging and healing and application to other HMAC mixture types were recommended. The other
system utilizes indirect tensile creep and strength testing with a longer gauge length than the
standard Superpave mixture test and visco-elastic analysis of material response (36, 37). The use
of fracture energy based on tests at 20 °C (68 °F) to predict fatigue cracking was validated using
data from the full-scale APT WesTrack project.
With a shift toward more mechanics-based approaches, fatigue analysis is expected to
become independent of many factors and variables that limit the application of ME approaches
that were the only available analysis tools prior to the rapid increase in computing power. These
factors and variables include mode of loading (controlled stress or controlled strain), laboratory
test type, time of loading, temperature, type and location of loading, rest periods, and HMAC
mixture variables.
Empirical to ME to Calibrated Mechanistic
A major reason for the gradual change of mixture fatigue analysis from empirical or
phenomenological to ME to calibrated mechanistic is the greatly increased capabilities of
computers to model material behavior realistically, using mechanics and user friendly
computational packages such as finite element programs. As computers become faster with
larger memories in the future, these approaches will be the simplest, most direct, and probably
most practical way to design HMAC mixtures and pavements.
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These computational packages can only utilize material properties as input, instead of
empirical constants or ME regression coefficients used in previous approaches. This
development brings with it an added bonus that laboratory or non-destructive field measurement
of material properties is much simpler than determination of these constants and coefficients
through extensive laboratory testing.
Calibrated Mechanistic Approaches. The calibrated mechanistic approaches are based
on the theory that HMAC is a complex composite material that behaves in a nonlinear visco-
elastic manner, ages, heals, and requires that energy be stored on fracture surfaces as load-
induced damage in the form of fatigue cracking progresses. Energy is also released from fracture
surfaces during the healing process. HMAC mixture resistance to fatigue cracking thus consists
of two components, resistance to fracture (both crack initiation and propagation) and the ability
to heal, that both change over time.
Several approaches that predict fatigue life require material characterization and account
for both the fracture and healing processes in HMAC that have been developed over the past
decade. In the SHRP A-005 project, a complete model of fatigue fracture and healing was
developed (38). Other researchers showed the importance of the use of fracture and dissipated
energy in measuring the fracture resistance of a HMAC mixture (39). This same concept of
dissipated energy per load cycle provides the driving force for fatigue crack initiation and
propagation, and researchers demonstrated that the fracture energy approach was able to
accurately predict the fatigue life of a wide variety of HMAC mixture designs as compared to
other approaches (40, 41). SHRP A-005 results and a finite element computer program have
been used to illustrate substantial agreement with these results in predicting the two phases of
crack growth, initiation, and propagation (42).
The Texas A&M Calibrated Mechanistic Approach. A micromechanical approach
developed at Texas A&M University based on the SHRP A-005 results requires only creep or
relaxation, strength, and repeated load tests in uniaxial tension and compression and a catalog of
fracture and healing surface energy components of asphalt binders and aggregates measured
separately (43, 44, 45).
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Surface energy components of various common aggregates and binders have been
measured at Texas Transportation Institute (TTI) in various studies (43, 44, 46, 47). The results
have been cataloged and are also proving useful in other ongoing TTI studies including moisture
damage prediction in HMAC pavements. In this approach selected for evaluation in this project,
HMAC behavior in fatigue is governed by the energy stored on or released from crack faces that
drive the fracture and healing processes, respectively, through these two different mechanisms.
Chapter 5 discusses this approach in greater detail.
Computational models that incorporate more realistic material behavior for HMAC are
expected to be increasingly faster and user-friendly in the near future. Convenient and efficient
methods of characterizing the fracture and healing properties of HMAC mixtures will be useful
to take advantage of these continued advances that promise improved mixture and pavement
design.
Binder Aging and HMAC Mixture Fatigue Resistance
TTI’s Center for Asphalt and Materials Chemistry (CMAC) has studied the effect of
oxidative aging on asphalt binders over the last 15 years. During this time, CMAC researchers
have conducted a comprehensive study of the oxidation kinetics of binders under varying
conditions of temperature and oxygen pressure and of the effect of this oxidation on the physical
properties of binders. Both of these issues are crucial to understanding the rate at which asphalt
binders age in service in the field and the results of these changes on performance. This section
briefly summarizes CMAC’s relevant results.
Fundamentally, the oxidation of binder results in compounds that are more polar and
therefore form strong associations with each other. These associations result in both a greater
resistance to flow (higher viscosity) and larger elastic modulus. Together these effects result in
higher stresses in HMAC under load. This greater resistance to flow can be beneficial at high
temperatures by reducing permanent deformation. A problem emerges, however, when aging is
excessive, leading to excessively large stresses that result in binder failure at lower temperatures
(thermal cracking).
Page 37
17
This effect of oxidative aging must also contribute to failure by repeated load (fatigue
cracking) through its effect on HMAC stiffness that governs material response to load. It also
explains why producing binders that have higher high-temperature Superpave grades (and thus
provide stiffer mixtures at rutting temperatures) may be more prone to premature fatigue
cracking. Starting out stiffer puts these HMAC mixtures at a disadvantage as stiffness
age-hardening proceeds throughout the lifetime of the HMAC pavement.
The following subsections provide more detail on these effects of oxidation on binders
and thus on HMAC mixture fatigue resistance.
Effect of Aging on Binder Viscosity
Binder viscosity increases dramatically due to oxidation, in fact, by orders of magnitude
over the life of a pavement. Figure 2-1 shows typical changes in the dynamic viscosity
master-curve for a binder at a reference temperature of 4 °C (39.2 °F). The effect is most
significant at high temperatures (low frequency) but plays a role in pavement performance at all
practical temperatures. The increase in log viscosity with oxidation is linear and has no bound
within the practical limits encountered by binder during a normal pavement life.
Figure 2-2 shows the increase in low shear-rate dynamic viscosity (η0*) measured at
60 °C (140 °F) versus aging time at 60 °C (140 °F) and atmospheric air pressure for two binders.
These data were obtained in thin films, and thus the hardening rates reflected by the slope of
these lines are higher than those that occur in the field, but the effect and ultimate result that is
dependent on binder type is clear nonetheless.
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18
10 6
10 7
10 8
10 9
10 10
10 11
10 12
10 -9 10 -7 10 -5 10 -3 10 -1 10 1 10 3
112 hr216 hr
η∗ (p
oise
)
Reduced Angular Frequency (rad/s)
Reference Temperature: 4 oC
SHRP AAB-1 Air B lowing: 93.3 oC
Figure 2-1. Master-Curve for SHRP AAB-1 at Two Aging Times
(°F = 32 + 1.8(°C)).
103
104
105
0 50 100 150 200 250
AAB-1 (Unaged)AAB-1 (RTFOT Aged)
AAB-1 (RTFOT plus 60 oC Aged)AAG-1AAG-1 (RTFOT Aged)
AAG-1 (RTFOT plus 60 oC Aged)
η0
* (60
°C
) (p
oise
)
Aging Time (60 oC, day)
Figure 2-2. Effect of Aging on Low Shear-Rate Limiting Viscosity
(°F = 32 + 1.8(°C)).
Page 39
19
Effect of Aging on Low-Temperature Superpave Performance Grade
Viscosity is inversely related to the m-value in the Superpave low-temperature
performance grade for binders and elastic modulus is related to stiffness. Thus as binders age, m
decreases and stiffness increases. This increase in stiffness (and decrease in m) results in a
deterioration of the low-temperature grade as a binder oxidizes (48). Figure 2-3 shows this
deterioration that results from extended exposure to long-term aging in the Pressure Aging
Vessel (PAV). Similar effects occur due to aging at pavement field conditions.
-32
-30
-28
-26
-24
-22
-20
-18
-16
-10 0 10 20 30 40 50
AAF-1AAS-1Exxon AC-10Exxon AC-20Shell AC-20
Con
tinuo
us B
ott
om G
rade
(o C)
PAV Aging Time in hours @ 100oC, 20 atm air Figure 2-3. Continuous Bottom Grade as a Function of PAV Aging Time
(°F = 32 + 1.8(°C)).
Effect of Aging on Ductility and Shear Properties
One of the significant results from the literature is that ductility at 15 °C (59 °F) relates
well to pavement performance (49, 50). According to these studies, when the ductility of a
binder decreases to a minimum value in the range of about of 3 to 5 cm (1.18 to 1.98 inches) (at
an extension rate of 1 cm/min (0.39 inches/min)), the pavement condition tends to suffer from
fatigue cracks. CMAC researchers have related this ductility to the dynamic shear rheometer
(DSR) loss (G’’) and storage moduli (G’). As these moduli increase, the binder breaks at smaller
values of strain (loss of ductility) due to higher values of stress.
Page 40
20
This correlation between ductility and the DSR function G′/(η′/G′) is shown in Figure 2-4
for some 20 conventional binders in the low ductility region thought to be near HMAC pavement
failure (51). The DSR function increases and the ductility decreases with oxidative aging.
TxDOT Project 0-1872 evaluated the correlation between this DSR function and field
performance (52).
1
1 0
1 0 -5 1 0 -4 1 0 -3 1 0 -2 1 0 -1
Duc
tilit
y (c
m) (
15 °
C, 1
cm
/min
)
G '/ (η '/G ') (M P a /s ) (1 5 °C , 0 .0 0 5 r a d /s )
Figure 2-4. Ductility versus DSR Function G’/(η’ /G’) (°F = 32 + 1.8(°C)).
Hypothetical Mechanisms
Based on the results described, CMAC researchers hypothesize a correlation between
oxidative aging and pavement failure by two mechanisms:
• Increased stresses under load (compared to new pavements) result from a decreased
ability to flow and an increased elastic stiffness, both leading to cracking.
• A decreased ability to self heal results in a decrease in fatigue life.
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21
Data described in this section lead to the following conclusion: oxidative aging produces
a material that is more susceptible to fatigue cracking or other distress that occurs later in the life
of the pavement. Consequently, an approach that predicts mixture fatigue resistance must be
sensitive to changes in binder properties that occur due to oxidative aging. These changes vary
for binder types that are different chemically and will thus exhibit different physical properties
over time depending on the effects of oxidation. Assessment of the impact of aging on HMAC
mixture fatigue resistance and the ability of different approaches to incorporate this effect in
predicting fatigue life is therefore important and thus selected as part of this project. Binder tests
and results are discussed in Chapters 8 through 11.
SELECTED FATIGUE ANALYSIS APPROACHES
Based on this extensive literature review and subsequent consultation with TxDOT
project personnel, the research team selected the following fatigue analysis approaches for
comparative evaluation in this project:
(1) The mechanistic empirical with flexural bending beam fatigue testing.
(2) The calibrated mechanistic with Surface Energy measurements.
(3) The calibrated mechanistic without surface energy measurements.
(4) The proposed NCHRP 1-37A 2002 Pavement Design Guide with dynamic modulus
testing.
These approaches together with binder aging effects are discussed in more detail in
Chapters 4, 5, 6, 7, and 8, respectively. Binder-mixture characterization that relates binder
oxidative aging to HMAC mixture fatigue properties is presented in Chapter 9.
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22
SUMMARY
The following bullets summarize the key points from the information search:
• Of the positive responses received, the field survey questionnaire indicated that the majority
of the DOTs use Superpave, mechanistic empirical, AASHTO, Asphalt Institute, and
visco-elastic continuum-damage analysis for their fatigue mixture design, analysis, and/or
structural design check with laboratory tests including the bending beam, dynamic modulus,
indirect tension, uniaxial fatigue, moisture sensitivity, and retained indirect tensile strength.
• A detailed literature review indicated that the major disadvantage of most ME approaches are
the lengthy test programs and the fact that these approaches are phenomenologically or
empirically based and often assume HMAC linear elastic behavior.
• With advances in computer technology, there has been a drive towards more simple and
realistic calibrated mechanistic approaches that utilize continuum micro-mechanics with
fracturing and healing as the two primary mechanisms governing HMAC fatigue damage.
Utilization of finite element analysis provides HMAC modeling the potential to include
visco-elastic behavior while calibration constants are used to realistically simulate field
conditions.
• Binder oxidative aging has a significant impact on HMAC pavement fatigue performance
primarily in terms of the HMAC mixture’s resistance to fracture under traffic loading and
ability to heal. The inclusion of aging in HMAC fatigue mixture designs is profoundly
significant.
• Four fatigue analysis approaches: ME, CMSE, CM, and the proposed NCHRP 1-37A 2002
Pavement Design Guide, were selected for comparative evaluation and subsequent
recommendation to TxDOT. This evaluation and recommendation are discussed in this
interim report.
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23
CHAPTER 3 EXPERIMENTAL DESIGN
The research methodology for this project involved an information search (discussed in
Chapter 2) and subsequent selection of fatigue analysis approaches, drafting an experimental
design program, laboratory testing, and subsequent data analysis. This chapter discusses the
experimental design including materials selection and the corresponding specimen fabrication
protocols and aging conditions. Field conditions in terms of the selected pavement structures,
traffic, and environmental conditions are also presented. Laboratory testing including the
appropriate fatigue analysis approaches and binder-mixture characterization are discussed in
Chapters 4 through 9, respectively.
HMAC MIXTURES AND MIX-DESIGN
HMAC mixtures commonly used by TxDOT include Type C, Coarse Matrix High Binder
(CMHB)-Type C, CMHB-Type F, Type A, Type B, Type D, Type F, Superpave, Stone Mastic
Asphalt (SMA), Stone Filled Mixture, and Porous Friction Course (PFC) (53). Type C and
CMHB-Type C are the most common. More specialized mixtures include the SMA and stone
filled designs developed to provide superior rutting performance.
Aggregates generally include limestone, igneous, and gravel characterized and blended to
typical TxDOT or Superpave standards. Among the Performance-Graded (PG) binders used by
TxDOT, notable ones include PG 58-22, PG 64-22, PG 70-22, and PG 76-22 for the
environmental conditions in Texas.
For this project, the research team selected two commonly used TxDOT HMAC mixtures
for comparative fatigue performance evaluation. These were basic TxDOT Type C and rut
resistant Superpave HMAC mixtures, defined as the Bryan (BRY) and Yoakum (YKM)
mixtures, respectively, to represent the districts where the mix designs were obtained. Note that
development of mix designs was not part of this project.
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24
The Bryan Mixture – Basic TxDOT Type C (PG 64-22 + Limestone)
The Bryan HMAC mixture was designed using standard TxDOT gyratory design
protocols from the Bryan District (54). This mixture consists of a performance-graded PG 64-22
binder mixed with limestone aggregates to produce a dense-graded TxDOT Type C mixture. The
aggregate gradation curve for this mixture is shown in Figure 3-1. This mixture was used on
highways US 290 and SH 47 in the Bryan District (54).
0
20
40
60
80
100
0 1 2 3 4 5
Sieve Size (k0.45)
% P
assi
ng
Specification Limits
Figure 3-1. Limestone Aggregate Gradation Curve for TxDOT Type C Mixture.
The PG 64-22 binder was supplied by Eagle Asphalt, and the limestone aggregate was
supplied by Colorado Materials, Inc. from its Caldwell plant. The mix design was 4.6 percent
binder content by weight of aggregate (4.4 percent by weight of total mix) with a HMAC
mixture theoretical maximum specific gravity of 2.419 (54). The target specimen fabrication air
void (AV) content was 7±0.5 percent to simulate after in situ field construction and trafficking
when fatigue resistance is critical.
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25
The Yoakum Mixture – Rut Resistant 12.5 mm Superpave (PG 76-22 + Gravel)
The Yoakum HMAC mixture from the Yoakum District was a 12.5 mm Superpave
mixture designed with a PG 76-22 binder and crushed river gravel. This mixture was used on US
Highway 59 near the City of Victoria in Jackson County and is considered a rut resistant
mixture. This type of HMAC mixture was selected to examine its fatigue properties consistent
with the title and motivation of this project.
The binder and aggregates were sourced from Eagle Asphalt (Marlin Asphalt), Inc. and
Fordyce Materials, respectively. Unlike PG 64-22, PG 76-22 is a modified binder with about 5
percent styrene-butadiene-styrene (SBS) polymer.
In addition to the crushed river gravel, the Yoakum mixture used 14 percent limestone
screenings and 1 percent hydrated lime. Figure 3-2 shows the combined dense gradation of the
Yoakum river gravel.
0
20
40
60
80
100
0 1 2 3 4
Size Size (k0.45)
% P
assi
ng
Restricted ZoneSpecification Limits
Figure 3-2. Gravel Aggregate Gradation Curve for Rut Resistant 12.5 mm Superpave
Mixture.
Page 46
26
The mix design was 5.6 percent binder content by weight of aggregate (5.3 percent by
weight of total mix) with a HMAC mixture theoretical maximum specific gravity of 2.410. Like
the Bryan mixture, the target specimen fabrication AV for the Yoakum HMAC mixture was
7±0.5 percent.
Material Properties for the Binders
Laboratory characterization of the binder materials based on the AASHTO PP1, PP6,
T313, and T315 test protocols produced the results shown in Figures 3-3 through 3-5 (55, 56).
These results represent mean values of at least two binder test samples.
Note that for most of the binder test results, metric units are used consistent with the PG
specifications used by TxDOT for binders (55, 56). English (U.S.) units or unit conversions are
provided in parentheses to meet TxDOT requirements for other units including length and
temperature.
100
1,000
10,000
52 58 64 70 76 82 88
Test Temperature, oC
G*/
Sin
(del
ta), P
asca
l
52 58 64 70 76 82 88
High Temperature PG Grade
PG 64-22PG 76-22
Threshold ≥ 1,000 Pascal
Figure 3-3. Binder High Temperature Properties – G*/Sin (delta) (Pascal)
(°F = 32 + 1.8(°C)), (delta ≅ δ).
Page 47
27
100
1,000
-24 -18 -12 -6
Test Temperature, oC
Cre
ep S
tiffn
ess,
MPa
-34 -28 -22 -16
Low Temperature PG Grade
PG 64-22PG 76-22
Threshold ≤ 300 MPa
Figure 3-4. Binder Low Temperature Properties – Flexural Creep Stiffness (MPa)
(°F = 32 + 1.8(°C)).
0.2
0.3
0.4
-24 -18 -12 -6
Test Temperature, oC
m-v
alue
-34 -28 -22 -16
Low Temperature PG Grade
PG 64-22PG 76-22
Threshold ≥ 0.30
Figure 3-5. Binder Low Temperature Properties (m-value)
(°F = 32 + 1.8(°C)).
These verification results shown in Figures 3-3 through 3-5 indicate that the binders meet
the PG specification consistent with the material properties for PG 64-22 and PG 76-22 binders
(55, 56).
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28
Table 3-1 shows the measured intermediate temperature properties of the binders at 25 °C
(77 °F) in terms of the complex shear modulus (G*) and the phase angle (δ). The results
represent average values of three replicate binder-sample tests. These properties quantify the
binders’ resistance to fatigue associated cracking. As shown in Table 3-1, both the PG 64-22 and
PG 76-22 met the required maximum specified threshold value of a G* Sin δ of 5,000 kPa
(55, 56).
Table 3-1. Intermediate Temperature Properties of the Binders at 25 °C (77 °F).
Average Value Binder
δ (°) G*Sin δ (kPa)
Standard Deviation of G*Sin δ
(kPa)
CV (G*Sin δ) (%)
PG Specification
(kPa)
PG 64-22 65 600 10.91 1.82 ≤ 5000
PG 76-22 62 1019 70 6.90 ≤ 5000
Note that these measured binder properties also constitute input parameters for the
proposed NCHRP 1-37A Pavement Design Guide Level 1 analysis discussed in subsequent
chapters. These material property results also indicate that, as expected, the complex shear
modulus and flexural stiffness of the modified PG 76-22 binder at any test temperature is
relatively higher than that of the PG 64-22.
Material Properties for the Aggregates
Material properties for the aggregates listed in Table 3-2 indicate that the aggregate meets
the specification consistent with the respective test methods shown in the table (57). The bulk
specific gravity for the combined aggregates was 2.591 and 2.603 for limestone and gravel,
respectively.
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29
Table 3-2. Aggregate Properties.
Test Parameter Limestone Gravel Specification Test Method
Soundness 18% 20% ≤ 30% Tex-411-A
Crushed faces count
100% 100% ≥ 85% Tex-460-A
Los Angeles (LA) abrasion 28% 25% ≤ 40% Tex-410-A
Sand equivalent 74% 77% ≥ 45% Tex-203-F
HMAC SPECIMEN FABRICATION
The basic HMAC specimen fabrication procedure involved the following steps: aggregate
batching, binder-aggregate mixing, short-term oven aging (STOA), compaction, sawing and
coring, and finally volumetric analysis to determine the AV. These steps are briefly discussed in
this section.
Aggregate Batching
Aggregates were batched consistent with the gradations shown in Tables 3-3 and 3-4,
which correspond to those shown in Figures 3-1 and 3-2, respectively.
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30
Table 3-3. Limestone Aggregate Gradation for TxDOT Type C Mixture.
Sieve Size TxDOT Specification (53)
mm Upper Limit (%) Lower Limit (%)
% Passing
5/8″ 15.9 100 98 100.0
1/2″ 12.5 100 95 100.0
3/8″ 9.5 85 70 84.8
#4 4.75 63 43 57.9
#10 2.0 40 30 36.9
#40 0.425 25 10 19.0
#80 0.175 13 3 5.0
#200 0.075 6 1 1.0
Table 3-4. Gravel Aggregate Gradation for 12.5 mm Superpave Mixture.
Sieve Size TxDOT Specification (53)
mm Upper Limit (%) Lower Limit (%)
% Passing
3/4″ 19.00 100 -- 100.01/2″ 12.50 100 90 94.63/8″ 9.50 90 81.0
#4 4.75 54.4#8 2.36 58 28 32.9
#16 1.18 22.4#30 0.60 16.2#50 0.30 11.0
#100 0.150 7.6#200 0.075 10 2 5.5
Page 51
31
Mixing, Short Term Oven-Aging, Compaction, and Air Voids
The HMAC mixture mixing and compaction temperatures shown in Table 3-5 are
consistent with the TxDOT Tex-205-F and Tex-241-F test specifications for PG 64-22 and
PG 76-22 binders (57). Prior to binder-aggregate mixing, the limestone and gravel aggregates
were pre-heated to a temperature of 144 °C (291 °F) and 163 °C (325 °F), respectively, for at
least 4 hrs to remove any moisture. The binder was also heated at the mixing temperature for at
most 30 minutes before mixing to liquefy it.
Table 3-5. HMAC Mixture Mixing and Compaction Temperatures.
HMAC Mixture Temperature (°C) Process
Bryan Mixture Yoakum Mixture
Aggregate pre-heating 144 (291 °F) 163 (325 °F)
Binder-aggregate mixing 144 (291 °F) 163 (325 °F)
4 hrs short-term oven aging 135 (275 °F) 135 (275 °F)
Compaction 127 (261 °F) 149 (300 °F)
HMAC mixture STOA lasted for 4 hrs at a temperature of 135 °C (275 °F), consistent
with the AASHTO PP2 standard aging procedure for Superpave mixture performance testing
(58). STOA simulates the time between HMAC mixing, transportation, and placement up to the
time of in situ compaction in the field (58). Note that the acronym AASHTO PP2 is also used
synonymously with the acronym STOA in this interim report.
Gyratory Compaction
All the cylindrical specimens for the Dynamic Modulus and CMSE/CM tests were
gyratory compacted using the standard Superpave Gyratory Compactor (SGC) shown in Figure
3-6. Compaction parameters were 1.25° compaction angle and 600 kPa (87 psi) vertical pressure
at rate of 30 gyrations per minute.
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32
Figure 3-6. Superpave Gyratory Compactor.
Kneading Beam Compaction
Researchers compacted beam specimens for the flexural bending beam fatigue tests using
the linear kneading compactor shown in Figure 3-7 up to the target AV content consistent with
the specified beam thickness at a maximum compaction pressure of 6900 kPa (1000 psi)
(11, 12).
Figure 3-7. Linear Kneading Compactor.
All HMAC specimens were compacted to a target AV content of 7±0.5 percent, as stated
previously, to simulate after in situ field construction and trafficking when fatigue resistance is
critical.
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33
Sawing, Coring, Handling, and Storage
Cylindrical specimens were gyratory compacted to a size of 165 mm (6.5 inches) height
by 150 mm (6 inches) diameter, while actual test specimens were sawn and cored to a 150 mm
(6 inches) height and 100 mm (4 inches) diameter. Beam specimens were kneading compacted to
a size of 457 mm (18 inches) length by 150 mm (6 inches) width by 63 mm (2.5 inches)
thickness, and test specimens were sawn to a 380 mm (15 inches) length by 63 mm (2.5 inches)
width by a 50 mm (2 inches) thickness (11). Figure 3-8 shows the dimensions of the final test
specimens (where 1 mm ≅ 0.039 inches).
150 mm
100 mm
380 mm
50 mm
Width = 63 mm
Beam
Cylindrical
Figure 3-8. Laboratory Test Specimens (Drawing not to Scale)
(1 mm ≅ 0.039 inches).
After the specimens were sawn and cored, volumetric analysis based on the fundamental
principle of water displacement was completed to determine the actual specimen AV. HMAC
specimens that did not meet the target AV content were discarded or used as dummies in trial
tests. In total, a cylindrical specimen took approximately 40 hrs to fabricate while a beam
specimen, because of the difficulty in sawing, took an additional 5 hrs. While beam specimens
require delicate handling, the cylindrical specimens are not as sensitive to handling. Prior to
laboratory testing, specimens were generally stored on flat surfaces in a temperature-controlled
room at approximately 20±2 °C (68±36 °F).
Page 54
34
BINDER AND HMAC MIXTURE AGING CONDITIONS
Researchers selected three aging conditions listed in Table 3-6 for this project for both
the binder and HMAC compacted specimens. Consistent with the Superpave procedure, all
HMAC mixtures were subjected to 4 hrs STOA, as discussed previously, prior to the simulated
aging period for the three selected aging conditions.
Table 3-6. Aging Conditions for Binders and HMAC Compacted Specimens.
Aging Condition
@ 60 °C (140 °F)
Description Comment
0 months Simulates time period just after in situ field construction at the end of compaction (58)
3 months Simulates 3 to 6 years of Texas environmental exposure (52)
6 months Simulates 6 to 12 years of Texas environmental exposure (52)
All HMAC mixtures
(prior to compaction)
were subjected to 4 hrs
STOA (AASHTO PP2).
The aging process for HMAC specimens involved keeping the compacted specimens in a
temperature-controlled room at 60 °C (140 °F) and at the same time allowing the heated air to
circulate freely around the specimens. This allowed for accelerated oxidative aging of the binder
within the HMAC specimens. An aging temperature of 60 °C (140 °F) was selected to accelerate
aging because this temperature realistically simulates the critical pavement service temperature
in Texas for HMAC aging. Based on previous research, the process also simulates the field
HMAC aging rate (52). Chapter 8 discusses the aging process for the binder in detail.
Figure 3-9 is a schematic illustration of the HMAC specimen aging conditions considered
in each respective fatigue analysis approach. The NCHRP 1-37A 2002 Pavement Design Guide
software encompasses a Global Aging Model that takes into account the aging effects, which are
discussed in Chapter 7. Therefore, it was deemed unnecessary to test aged specimens for the
proposed NCHRP 1-37A 2002 Pavement Design Guide fatigue analysis.
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35
ME
, CM
SE, &
CM
All HMAC Mixtures:
Subjected to AASHTO PP2 @ 135 °C for 4 hrs
Age HMAC compacted specimens @ 60 °C for 0 months
(Total aging period = PP2 + 0 months)
Age HMAC compacted specimens @ 60 °C for 3 months
(Total aging period = PP2 + 3 months)
Age HMAC compacted specimens @ 60 °C for 6 months
(Total aging period = PP2 + 6 months)
Des
ign
Gui
de
Glo
bal A
ging
Mod
el
Figure 3-9. Fatigue Analysis Approaches and HMAC Mixture Aging Conditions
(°F = 32 + 1.8(°C)).
HYPOTHETICAL FIELD PAVEMENT STRUCTURES AND TRAFFIC
Table 3-7 displays a list of the five selected TxDOT pavement structures (PS) and five
associated traffic levels ranging between 0.25 to 11.00 × 106 equivalent single axle loads
(ESALs) that were considered in this project. These pavement structures represent actual
material properties and layer thicknesses that are commonly used on TxDOT highways (60).
Typical traffic conditions consisted of an 80 kN (18 kip) axle load, 690 kPa (100 psi) tire
pressure, 97 km/hr (60 mph) speed, and about 10 to 25 percent truck traffic over a design life of
20 years (60). In Table 3-7, PS# 5 represents the actual pavement structure where the Bryan
mixture was used.
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36
Table 3-7. Selected Pavement Structures and Traffic.
Material Type, Layer Thickness, and Elastic Modulus PS# Surfacing Base Subbase Subgrade
Traffic ESALs
% Trucks
1 HMAC, 6 inches, 500,000 psi
Flex, 14 inches*, 28,000 psi**
- 9000 psi 5,000,000 25
2 HMAC, 2 inches, 500,000 psi
Flex, 10 inches, 60,000 psi
Lime stabilized, 6 inches, 35,000 psi
12,400 psi 1,399,000 23.7
3 HMAC, 2 inches, 500,000 psi
Asphalt stabilized, 7 inches, 500,000 psi
Flex, 8 inches, 24,000 psi
Silt-clay, 9600 psi 7,220,000 13
4 HMAC, 2 inches, 500,000 psi
Flex, 6 inches, 50,000 psi
Stabilized subgrade, 5 inches, 30,000 psi
10,000 psi 390,000 10.7
5 US 290 HMAC, 4 inches, 500,000 psi
Cemented, 14 inches, 150,000 psi
- 15,000 psi 10,750,000 15.2
*1 inch ≅ 25.4 mm. ** 1 psi ≅ 0.0069 MPa
ENVIRONMENTAL CONDITIONS
Figure 3-10 shows five Texas environmental zones based on annual precipitation, annual
freezing index, and the number of wet days and freeze/thaw days (60). As shown in Figure 3-10,
the TxDOT districts have been grouped into five environmental zones namely; Dry-Cold (DC),
Wet-Cold (WC), Dry-Warm (DW), Wet-Warm (WW), and Moderate.
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37
Figure 3-10. Texas Environmental Zoning (60).
The italicized environmental zones (DC, WW, and DW) in Figure 3-10 indicate zones that
are critical to alligator (fatigue) cracking according to the TxDOT Pavement Management
Information System (PMIS) report (61). Based on this PMIS report, 20 to 100 percent of the
PMIS pavement sections in these locations exhibited alligator (fatigue) cracking.
AMA
SAT
LRD
PHR
CRP
YKM
HOU ELP
ODA
SJT AUS
WAC BWD
LBB ABL
CHS WFS
BMT
LFK
ATL FTW
DAL
TYL
PAR
Dry-Warm (DW)
Dry-Cold (DC)
Wet-Cold (WC)
Wet-Warm (WW)
Moderate (M)
Page 58
38
Pavement material performance depends on both traffic and environment. It is therefore
not uncommon that for a given design traffic level, a material that performs well in a particular
environment may perform poorly in a different environmental location. Material properties for
pavement design and performance evaluation are thus generally characterized as a function of
environmental conditions.
HMAC, for instance, is very sensitive to temperature changes, while unbound materials
in the base, subbase, or subgrade are generally more sensitive to moisture variations. Most often,
the HMAC elastic modulus is characterized as a function of seasonal or monthly temperature
variations, with the critical pavement temperature being at the mid-depth or two-thirds depth
point in the HMAC layer. This pavement temperature generally exhibits a decreasing trend with
depth. The subgrade elastic modulus is normally characterized as a function of the seasonal
moisture conditions, with the wettest period of the year as the worst-case scenario assuming a
conservative design approach. Note also that water seepage through cracks and/or accumulation
in AV can accelerate damage, including fatigue cracking in HMAC materials.
In this project, two environmental conditions, WW and DC were considered (Figure 3-
10). WW and DC are the two extreme Texas weather conditions the research team considered to
have a significant impact on HMAC mixture fatigue performance. In fact, the 2003 TxDOT
“Condition of Texas Pavements PMIS Annual Report” indicates that highway pavements in
these environmental locations (WW and DC) are comparatively more susceptible to fatigue-
associated cracking (61).
RELIABILITY LEVEL
For this project, the research team selected and utilized a reliability level of 95 percent.
This is a typical value used for most practical HMAC pavement designs and analyses. In
statistical terms, this means that for a given test or assessment criteria, there is 95 percent pass
expectance or data accuracy, and that up to 5 percent failure or result inaccuracy is anticipated
and tolerable. In simpler terms, for a 95 percent reliability level, it means that the acceptable risk
level is 5 percent.
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ELSYM5 STRESS-STRAIN ANALYSIS
For the five selected hypothetical PSs and environmental conditions (WW and DC)
considered, elastic ELSYM5 stress-strain computations were adjusted based on FEM simulations
to account for the HMAC visco-elastic behavior (62, 63).
ELSYM5 Input and Output Data
The bullets below summarize the typical input data requirement for ELSYM5 analysis:
• pavement structure (i.e., number of layers and layer thicknesses),
• material properties (i.e., elastic modulus and Poisson’s ratio), and
• Traffic loading (i.e., axle load and tire pressure).
Table 3-7 displayed the PSs and the respective elastic moduli used for ELSYM5 analysis
in this project. The axle load and tire pressure used were as discussed previously, 80 kN and
690 kPa. Typical Poisson’s ratios used by the researchers in the analysis were 0.33, 0.40, and
0.45 for the HMAC layer, the base, and subgrade, respectively (64).
The basic output response parameters from the ELSYM5 computational analysis include
the stresses, strains, and deformations. The strain response parameters were, however, adjusted
according to FEM simulations discussed in the subsequent text to account for HMAC
visco-elastic behavior.
These tensile (εt) and shear (γ) strains constitute input parameters for the ME, CMSE, and
CM fatigue analysis, respectively, discussed in Chapters 4 through 6. Stress-strain computations
for the proposed NCHRP 1-37A 2002 Pavement Design Guide (Chapter 7) is built into the
analysis software.
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FEM Strain-Adjustment
The FEM strain-adjustment factor for elastic strain analysis to account for HMAC
visco-elastic behavior was determined as follows:
5)(
ELSYM
FEMiVEadj Strain
StrainS = (Equation 3-1)
where:
Sadj(VE) = FEM strain-adjustment factor for HMAC visco-elastic behavior
StrainFEM = Strain (εt or γ) computed via FEM analysis (mm/mm)
StrainELSYM5 = Strain (εt or γ) computed via ELSYM5 analysis (mm/mm)
Subscript i = Stands for εt or γ
For this project, Sadj(VE) values of 1.25 and 1.175 were used for εt and γ, respectively,
based on the previous FEM work by Park (63, 65). Note that while it is possible that these
visco-elastic adjustments may vary for different mixtures, the adjustment from layered elastic to
elasto-viscoplastic was assumed to be constant across both mixtures in this project. In addition,
the elastic moduli values at 0 months aging for these two mixtures did not vary significantly.
Thus for each computed ELSYM5 strain (εt and γ) for the PSs shown in Table 3-7, the Sadj(VE)i
was applied as follows:
( ) ( 5) ( 5)1.25tt adj VE e t ELSYM t ELSYMSε ε ε= × = (Equation 3-2)
( ) ( 5) ( 5)1.175adj VE ELSYM ELSYMS γγ γ γ= × = (Equation 3-2)
An example of the resulting strains (εt and γ) for the PSs shown in Table 3-7 for both
WW and DC environments is shown in Table 3-8.
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Table 3-8. Computed Critical Design Strains.
WW Environment DC Environment PS#
Tensile strain
(εt)
Shear strain
(γ)
Tensile strain
(εt)
Shear strain
(γ)
1 1.57 × 10-4 1.56 × 10-2 1.51 × 10-4 1.51 × 10-2
2 2.79 × 10-4 1.98 × 10-2 2.71 × 10-4 1.89 × 10-2
3 2.73 × 10-4 1.91 × 10-2 2.66 × 10-4 1.86 × 10-2
4 2.89 × 10-4 2.06 × 10-2 2.78 × 10-4 1.96 × 10-2
5 0.98 × 10-4 1.41 × 10-2 0.91 × 10-4 1.46 × 10-2
SUMMARY
Salient points from this chapter are summarized as follows:
• Two commonly used TxDOT HMAC mixtures, Bryan (PG 64-22 + limestone) and Yoakum
(PG 76-22 + gravel) mixtures were selected for fatigue analysis in this project. Bryan is a
normal basic TxDOT Type C HMAC mixture, while Yoakum is a Rut Resistant 12.5 mm
Superpave HMAC mixture. Both the binder and aggregate material properties were
consistent with the Superpave PG and TxDOT standards.
• Two laboratory compactors, the standard SGC and kneading beam, were utilized for
compacting cylindrical and beam HMAC specimens, respectively. The target specimen
fabrication AV content was 7±0.5 percent to simulate the in situ AV field compaction after
construction and trafficking when fatigue resistance is critical.
• Three aging conditions for both binders and HMAC mixtures at a critical temperature of
60 °C (140 °F) were selected to investigate the effects of oxidative aging on binder and
HMAC mixture fatigue properties, including fatigue life. These aging conditions were 0, 3,
and 6 months that simulate up to 12 years of Texas environmental-field HMAC aging.
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• Five commonly used TxDOT HMAC pavement structures with corresponding traffic levels
of 0.25 to 11.00 million ESALs and 10 to 25 percent truck traffic were selected for analysis.
Using layered elastic analyses (ELSYM5) and adjusting based on FEM simulations, tensile
and shear strains within the pavement HMAC layer were determined and utilized as the
failure load-response parameters associated with fatigue cracking when predicting the
HMAC mixture fatigue resistance.
• Two Texas environmental conditions (Wet-Warm and Dry-Cold) critical to fatigue
associated (alligator) cracking in HMAC pavements were selected for the analysis.
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CHAPTER 4 THE MECHANISTIC EMPIRICAL APPROACH
This chapter discusses the mechanistic empirical approach for HMAC pavement fatigue
analysis including the fundamental theory, input/output data, required flexural bending beam
laboratory testing, failure criteria, analysis procedure, and variability.
FUNDAMENTAL THEORY
The selected SHRP A-003A ME approach in this project utilizes the flexural bending
beam fatigue test (third-point loading) and considers bottom-up cracking to determine an
empirical fatigue relationship of the simple power form shown in Equation 4-1 (25).
2
1kkN −= ε (Equation 4-1)
where:
N = Number of load cycles to fatigue failure
ε = Applied tensile strain (mm/mm)
ki = Laboratory determined material constants
The SHRP A-003A fatigue analysis approach incorporates reliability concepts that
account for uncertainty in laboratory testing, construction, and traffic prediction; and considers
environmental factors, traffic loading, and pavement design. The SHRP A-003A is the ME
fatigue analysis approach utilized in this project, and the BB testing to determine the HMAC
mixture fatigue empirical relationship shown in Equation 4-1 was based on the AASHTO
TP8-94 test protocol (59, 66). The AASHTO TP8-94 test protocol is discussed later in this
chapter.
HMAC specimen preparation by rolling or kneading wheel compaction is strongly
recommended as part of this ME approach to simulate the engineering properties of extracted
field pavement cores. Conditioning prior to testing to a representative or worst-case aging state is
also suggested.
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The AASHTO TP8-94 test protocol requires testing conditioned specimens at two
different controlled strain levels under sinusoidal repeated loading to generate an empirical
fatigue relationship, as shown in Equation 4-1 (59).
Determination of the experimental fatigue relationship, as expressed by Equation 4-1,
constitutes the empirical part of the ME approach of fatigue modeling of HMAC mixtures. This
empirical fatigue relationship (Equation 4-1) is then used in the design and analysis system
illustrated schematically in Figure 4-1.
ME FATIGUE ANALYSIS
Pavement structure
Pavement materials
Traffic
Environment
Trial HMAC mix
Nf (Mixture Fatigue Resistance) Nf(Demand)
Empirical fatigue relationship
Design strain
Shift factor
Temperature correction factor
Reliability multiplier (M)
Traffic ESALs
Nf ≥ M × Traffic ESALs
YES
NO
Final Fatigue Design
Figure 4-1. The ME Fatigue Design and Analysis System.
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The fatigue analysis system shown in Figure 4-1 evaluates the likelihood that the selected
design HMAC mixture will adequately resist fatigue cracking in a specific pavement structure
under anticipated in situ conditions including traffic and environment. The designer must,
however, select a specific level of reliability commensurate with the pavement site for which the
mixture will be utilized as well as the required level of service of the pavement structure.
A HMAC mixture is expected to perform adequately if the number of load repetitions
sustainable in laboratory testing after correcting for field conditions exceeds the number of load
repetitions anticipated in service. The design strain at which the pavement fatigue life must be
estimated using the empirical fatigue relationship developed based on laboratory test results is
often computed using a simple multilayer elastic theory. For this computation, the design strain
of interest is the maximum principal tensile strain at the bottom of the HMAC layer in the
specific pavement structure, assuming the bottom-up mode of fatigue cracking. The
determination of this field critical design tensile strain within a representative field pavement
structure at the bottom of the HMAC layer constitutes the mechanistic part of the ME approach.
INPUT/OUTPUT DATA
Table 4-1 summarizes the general ME fatigue analysis input and the expected output data
based on the SHRP A-003A approach and the AASHTO TP8-94 BB test protocol (59). These
parameters and their respective components are discussed in more detail in subsequent sections.
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Table 4-1. Summary of ME Fatigue Analysis Input and Output Data.
Source Parameter
Laboratory test data (HMAC mixture testing of beam specimens)
- Strain (εt) & stress - # of fatigue load cycles (N)
Analysis of laboratory test data
- Flexural stiffness or dissipated energy - Empirical fatigue relationship (N = f(εt))
Field conditions (design data)
- Pavement structure (layer thickness) - Pavement materials (elastic modulus & Poisson’s ratio) - Traffic (ESALs, axle load, & tire pressure) - Environment (temperature & moisture conditions) - Field correction/shift factors (i.e., temperature)
Computer stress-strain analysis
- Design tensile strain (εt) @ bottom of the top HMAC layer
Other - Reliability level (i.e., 95%) - Reliability multiplier (M)
OUTPUT - HMAC mixture fatigue resistance (Nf(Supply)) - Pavement fatigue life (Nf(Demand)) - Assessment of adequate or inadequate performance
LABORATORY TESTING
The BB fatigue test, including the test equipment, specimen setup, and data acquisition,
was conducted consistent with the AASHTO TP8-94 test procedure (11, 12). This section
summarizes the BB fatigue test protocol.
The BB Fatigue Test Protocol
The BB fatigue test consists of applying a repeated constant vertical strain to a beam
specimen in flexural tension mode until failure or up to a specified number of load cycles. In this
project, the test was strain controlled, and the input strain waveform was sinusoidal shaped,
applied at a frequency of 10 Hz. The BB device and the loading configuration are shown in
Figures 4-2 and 4-3, respectively.
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Figure 4-2. The Bending Beam (BB) Device.
0 0.2 0.4 0.6 0.8 1 1.2
Time, s
Stra
in
0.5F 0.5F
Deflection
Figure 4-3. Loading Configuration for the BB Fatigue Test.
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As evident in Figure 4-3, repeated vertical loading causes tension in the bottom zone of
the specimen, from which cracking will subsequently initiate and propagate, thus simulating
pavement fatigue failure under traffic loading. The test was conducted at two strain levels of
approximately 374 and 468 microstrains (i.e., an equivalence of 0.20 and 0.25 mm deflections,
respectively), consistent with the AASHTO TP8-94 test protocol to generate the required
material N-εt empirical relationship shown in Equation 4-1 (59). These test strain levels are
within the recommended AASHTO TP8-94 test protocol range to reduce test time while at the
same time capturing sufficient data for analysis.
A 10 Hz frequency (Figure 4-3) without any rest period was used for the test. The
average duration of each test was approximately 5 hrs. Note that the BB test time is inversely
proportional to the magnitude of the input strain wave. Testing can, however, be terminated
either when the initial application load response (stress) recorded at the 50th load cycle decreases
to 50 percent in magnitude or when a preset number of load cycles such as 100,000 is reached.
The former approach was used in this project.
Test Conditions and Specimens
HMAC is temperature sensitive, so the test was conducted in an environmentally
controlled chamber at a test temperature of 20±0.5 °C (68 ±32.9 °F), consistent with the
AASHTO TP8-94 test procedure (59). The minimum specimen conditioning time was 2 hrs.
However, specimens were actually preconditioned at 20 °C (68 °F) on a more convenient 12 hrs
overnight-time period. The test temperature was monitored and recorded every 600 s via a
thermocouple probe attached inside a dummy specimen also placed in the environmental
chamber. Figure 4-4 is an example of a temperature plot captured during the BB test at 20 °C
(68 °F).
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Tmean, 19.96
TLower Limit, 19.50
TUpper Limit, 20.50
19.00
19.50
20.00
20.50
21.00
0 6,000 12,000 18,000
Time, s
Tem
pera
ture
, oC
Figure 4-4. Example of Temperature Plot for the BB Test.
As evident in Figure 4-4, the average temperature for this particular test was 19.96 °C
(67.93 °F) with a coefficient of variation of 0.84 percent. Three replicate beam specimens were
tested for each strain level, so a complete BB test cycle for low and high strain level tests
required a minimum of six beam specimens per aging condition per mixture type.
Test Equipment and Data Measurement
A servo electric-hydraulic controlled material testing system (MTS) equipped with an
automatic data measuring system applied the sinusoidal input strain waveform. Actual loading of
the specimen was transmitted by the BB device shown in Figure 4-2, to which the beam
specimen is securely clamped.
Loading data were measured via the MTS load cell, and flexural deflections were
recorded via a single linear differential variable transducer (LVDT) attached to the center of the
specimen. During the test, load and flexural deformation data were captured electronically every
0.002 s. Figure 4-5 is an example of the output stress response from the BB test at 20 °C (68 °F)
based on a 374 test microstrain level.
Page 70
50
100
150
200
250
0 4,000 8,000 12,000 16,000
Time, s
Stre
ss, p
si
Figure 4-5. Example of Stress Response from BB Testing at 20 °C (68 °F)
(374 microstrain level).
FAILURE CRITERIA
For HMAC compacted specimens subjected to repeated flexural bending, failure is
defined as the point at which the specimen flexural stiffness is reduced to 50 percent of the initial
flexural stiffness (59, 66). This initial stiffness is generally defined as the specimen flexural
stiffness measured at the 50th load cycle. With this criterion, fatigue cracking was considered to
follow the bottom-up failure mode assuming a service temperature of 20 °C (68 °F).
ANALYSIS PROCEDURE
The ME fatigue analysis utilized in this project was a five-step procedure involving
laboratory test data analysis to determine the HMAC Nf-εt empirical relationship expressed by
Equation 4-1, computer stress-strain analysis to determine the design maximum εt within a
selected and representative pavement structure at the bottom of the HMAC layer, statistical
analysis to predict the design HMAC mixture fatigue resistance, determination of the required
pavement life, and finally, a design check for adequate performance. These analyses, which are
illustrated schematically in Figure 4-1, are discussed in this section.
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Step 1: Laboratory Test Data Analysis (N-εt Empirical Relationship)
Laboratory test data from the BB fatigue test, which is discussed subsequently, was
analyzed using the AASHTO TP8-94 calculation procedure. Equations 4-2 to 4-4 are the
fundamental basis for BB test data analysis (59).
t
tSεσ
= (Equation 4-2)
1
%50
%50 69315.0ln
−−=⎟⎠⎞
⎜⎝⎛
= bbA
S
N (Equation 4-3)
where:
S = Flexural stiffness (MPa)
σt = Maximum measured tensile stress per load cycle (kPa)
εt = Maximum measured tensile strain per load cycle (mm/mm)
N50% = Number of load cycles to failure during BB testing
S50% = Flexural stiffness at failure during BB testing (MPa)
A = Initial peak flexural stiffness measured at the 50th load cycle (MPa)
b = Exponent constant from log S versus log load cycles (N) plot
The solution of Equation 4-3 for two different input strain levels (i.e., low and high), and
a plot of the resultant N50% versus the respective applied εt on a log-log scale will generate the
required empirical fatigue relationship of the simple power form shown in Equation 4-1.
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Step 2: Stress-Strain Analysis, εt (Design)
Following establishment of the HMAC Nf-εt empirical relationship through laboratory
test data analysis, computer stress-strain analysis was executed to determine the actual maximum
design εt of a given pavement structure at the bottom of the HMAC layer. Input parameters for
this analysis include traffic loading, pavement structure (layer thicknesses), material properties,
and the desired response location, which in this project was (t – 0.01), where t is the thickness of
the top HMAC layer in inches (or mm, where 1 inch ≅ 25.4 mm). Traffic loading data include
the standard axle load (e.g., 80 kN [18 kip]), ESALs, and axle and tire configurations. Material
properties including the elastic modulus and Poisson’s ratio should be defined as a function of
the environment in terms of temperature and subgrade moisture conditions.
In this project, a user-friendly and simple multi-layer linear-elastic software, ELSYM5,
was used for εt computations at the bottom of the HMAC layer (62). Ideally, a FEM software
that takes into account the visco-elastic nature of the HMAC material is desired for this kind of
analysis. Consequently, adjustments were applied to the ELSYM5 linear-elastic analysis results,
consistent with the FEM adjustment criteria discussed in Chapter 3.
Step 3: Statistical Prediction of HMAC Mixture Fatigue Resistance, Nf(Supply)
Nf(Supply) is the laboratory design HMAC mixture fatigue resistance that was statistically
determined as a function of the design εt (ELSYM5 analysis) and the laboratory determined
empirical fatigue N-εt (Equation 4-1) relationship at a given reliability level. This is discussed in
great detail in the subsequent section.
While Nf(Supply) represents laboratory fatigue life, the final field fatigue life for this ME
approach in this project was obtained as expressed by Equation 4-4.
[ ]( )TCFNSF
TCFkSF
N Supplyfk
tif
)(2 ×
==−ε
(Equation 4-4)
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where:
TCF = Temperature conversion factor to laboratory test temperature
SF = Shift factor that accounts for traffic wander, construction variability, loading frequency, crack propagation, and healing
For simplicity, TCF and SF values of 1.0 and 19, respectively, were used in this project
(1, 2). Determination of these parameters generally requires local calibration to field conditions,
which was beyond the scope of this project.
Step 4: Determination of the Required Pavement Fatigue Life, Nf(Demand)
Nf(Demand) is the expected pavement fatigue life, which is representative of the actual
applied traffic loading. It is a function of the total traffic ESALs summed over the entire
pavement design life determined as expressed by Equation 4-5.
)()( DesignDemandf ESALsTrafficMN ×= (Equation 4-5)
where:
M = Reliability multiplier
In the ME fatigue analysis approach, the safety factor associated with a specified level of
reliability is often defined in terms of reliability multiplier (M) and applied to traffic demand
(i.e., ESALs) as shown in Equation 4-5 (1, 2). This factor accounts for mixture variability and
the anticipated uncertainties in traffic estimate (demand) and mixture fatigue resistance (supply)
and performance during service. For a reliability level of 95 percent, some studies have used an
M value of 3.57, and this was the value used in this study (1, 2).
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Step 5: Fatigue Design Check for Adequate Performance
A fatigue design check for adequate performance requires that the HMAC mixture
fatigue resistance be greater than or equal to the required pavement fatigue life as expressed by
Equation 4-6.
)(Demandff NN ≥ (Equation 4-6)
If Nf is less than Nf(Demand), a wide range of options including the following are available:
• redesigning the HMAC mixture by changing the binder content and/or type, AV,
aggregate type or gradation;
• redesigning the pavement structure by changing the layer thicknesses, for example;
• redesigning the underlying pavement materials including the subbase, base, and/or
subgrade,
• reducing the pavement design life; and/or
• allowing an increased risk of premature failure.
VARIABILITY, STATISTICAL ANALYSIS, AND Nf PREDICTION
Precision is inversely proportional to uncertainty/variability in a testing method. If N is
the measured fatigue life and f(supply)N is the predicted fatigue life at a given design strain level,
then the precision of the method (on a log scale) can be represented by the estimated variance of
[ ]f(supply)NLn as follows:
( )( ) ⎟
⎟⎠
⎞⎜⎜⎝
⎛
−−
++=∑
∗ 2
222 11
xxqxX
nss
py
(Equation 4-7)
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55
where:
y* = [ ]f(supply)NLn
2∗y
s = Estimated variance of [ ]f(supply)NLn
s2 = ( )[ ]NLnVar
n = Number of test specimens
X = Ln[in situ strain] at which [ ]f(supply)NLn must be predicted
x = Average Ln[test strain]
q = Number of replicate specimens at each test strain level
xp = Ln[strain] at the pth test strain level
A prediction interval for [ ]f(supply)NLn is another way of assessing the precision of the
prediction. If the resulting interval is narrow, there is little uncertainty in [ ]f(supply)NLn , and the
prediction is quite precise. An explicit formula for a 1-α prediction interval for the linear
regression exists as follows:
∗−−±+yn stbXa 2,2/1 α (Equation 4-8)
where:
a, b = The estimated intercept and the estimated slope of the least squares
line fitted on the ( ) ( )( )fNLnstrainLn , data
2,2/1 −− nt α = The t-critical value corresponding to the right tail probability of
2α of the t distribution with n-2 degrees of freedom 2
∗ys = The estimated variance of [ ]f(supply)NLn as given in Equation 4-7
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The estimated intercept and the estimated slope, a and b, respectively, can also be given
explicitly as follows:
xbya += (Equation 4-9)
and
( )( )( )∑
∑−
−−= 2xxq
yyxxqb
p
pp (Equation 4-10)
where:
yp = ( )NLn at the pth test strain level
y = Average ( )NLn
Note that the predicted fatigue life [ ]f(supply)NLn or the prediction interval estimate
[ ]∗∗ −−−− ++−+ynyn stbXastbXa 2,2/12,2/1 , αα can be back-transformed by taking ( )exp to provide
the estimates in the original scale, but the variance estimate 2∗y
s itself cannot be transformed in
the same manner.
In summary, Ln Nf(supply) values were predicted based on the least squares line regression
analysis. Next, a 95 percent Ln Nf prediction interval was estimated based on the selected 95
percent reliability level. The predicted value and the prediction interval estimate estimates for
Nf(supply) were then obtained by back-transformation. As another measure of variability, a
coefficient of variation (COV) of Ln Nf was computed based on the estimated standard deviation
for the predicted Ln Nf value and the predicted mean Ln Nf value.
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SUMMARY
This section summarizes the ME fatigue analysis approach as utilized in this project.
• The ME approach is mechanistic empirical and based on the fundamental concepts that
fatigue cracking in HMAC pavements occurs due to critical tensile strains (εt) at the bottom
of the HMAC layer and that the predominant mode of crack failure is bottom-up crack
growth.
• Laboratory determination of the experimental N-εt fatigue relationship (i.e., the ki constants)
constitutes the empirical part of the ME approach, and determination of the field critical
design εt within a representative field pavement structure at the bottom of the HMAC layer
constitutes the mechanistic part.
• The flexural bending beam fatigue test conducted at 20 °C (68 °F) and 10 Hz in sinusoidal
strain-controlled mode is the principal HMAC mixture fatigue characterization test for the
ME approach. Under this BB testing, kneading or rolling compacted beam specimens are
required.
• For HMAC compacted specimens subjected to repeated flexural bending, fatigue failure
according to the ME approach is defined as the number of repetitive load cycles at which the
specimen flexural stiffness is reduced to 50 percent of the initial flexural stiffness measured
at the 50th load cycle.
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CHAPTER 5 THE CALIBRATED MECHANISTIC APPROACH
WITH SURFACE ENERGY
In this chapter, the calibrated mechanistic approach with surface energy including the
fundamental theory, input/output data, laboratory testing, failure criteria, analysis procedure, and
variability is discussed.
FUNDAMENTAL THEORY AND DEVELOPMENT
HMAC is a complex composite material that behaves in a non-linear visco-elastic
manner, ages, heals, and requires that energy be stored on fracture surfaces as load-induced
damage in the form of fatigue cracking. Energy is also released from fracture surfaces during the
healing process. HMAC mixture resistance to fatigue cracking thus consists of two components,
resistance to fracture (both crack initiation and propagation) and the ability to heal, processes
that both change over time. Healing, defined as the closure of fracture surfaces that occurs
during rest periods between loading cycles, is one of the principal component of the laboratory-
to-field shift factor used in traditional empirical fatigue analysis. Prediction of fatigue life or the
number of cycles to failure (Nf) must account for this healing process that affects both the
number of cycles for microcracks to coalesce to macrocrack initiation (Ni) and the number of
cycles for macrocrack propagation through the HMAC layer (Np) that add to Nf. Both
components of mixture fatigue resistance or the ability to dissipate energy that causes primarily
fracture at temperatures below 25 °C (77 °F), called dissipated pseudo strain energy (DPSE), can
be directly measured in simple uniaxial tensile and compression tests (5-6, 43-44,67).
The CMSE approach is a micromechanical approach developed at Texas A&M
University based on the SHRP A-005 results (44-45). The approach characterizes HMAC
materials both in terms of fracture and healing processes, and requires only creep or relaxation
tests in uniaxial tension and compression, strength and repeated load tests in uniaxial tension,
and a catalog of fracture and healing surface energy components of binders and aggregates
measured separately.
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In this CMSE approach, HMAC behavior in fatigue is governed by the energy stored on
or released from crack faces that drive the fracture and healing processes, respectively, through
these two mechanisms of fracture and healing.
DPSE and pseudo strain are defined to quantify and monitor fracture and healing in
HMAC mixtures. DPSE in an undamaged non-linear visco-elastic material is expected due to
the viscous lag in material response. This pseudo strain energy is represented by the area in the
pseudo hysteresis loop of a measured stress versus calculated PS after correcting for
non-linearity, plotted as shown in Figure 5-1. Pseudo strain is determined by calculating the
expected stress in a linear visco-elastic material under damaged conditions and dividing by a
measured reference modulus (from the first stress cycle of a repeated load test), and a non-
linearity correction factor (ψ(t)). This ψ(t) is introduced to account for any non-linearity of the
undamaged visco-elastic material (68).
Any departure from the initial pseudo hysteresis loop requires additional dissipated
energy, indicating that fracture is occurring for temperatures less than 25 °C (77 °F). As fracture
progresses with additional load cycles, DPSE will increase, while the HMAC mixture stiffness
will decrease. The healing process, on the other hand, produces opposite results, with DPSE
decreasing and the HMAC mixture stiffness increasing.
Pseudo Strain (calculated)
Stress (measured)
Figure 5-1. Example of Hysteresis Loop (Shaded Area is DPSE).
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Monitoring of both DPSE and PS in repeated uniaxial tension tests is required in this
micromechanical CMSE approach. The relationship between DPSE and N is modeled using
either of two functional forms, linear logarithmic or simple power law, and calibrated using
measured data. In this project, the research team used the former functional form, linear
logarithmic.
These calibration coefficients and Paris’ Law fracture coefficients determined by
monitoring both DPSE and PS with microcrack growth are required to determine Ni for
macrocrack initiation at an average microcrack size of 7.5 mm (0.30 inches) (67, 69). This
calibration is required because the coefficients of the equation for microcrack growth are not
widely known as compared to those for macrocrack growth. The size and shape of a microcrack
is controlled by microscopic quantities such as mastic film thickness, aggregate particle size, and
the degree of bonding of crack-arresting obstacles dispersed in the mastic. Nevertheless,
microcrack growth is still controlled by the rate of change of DPSE and indicated by a reduction
in HMAC mixture stiffness.
Np for microcrack propagation is a function of the difference between fracture and
healing speed. This Np is primarily quantified in terms of Paris’ Law fracture coefficients
(A and n) and the shear strain. Fracture speed depends on material properties determined in
uniaxial tensile creep or relaxation and strength tests at multiple temperatures and total fracture
surface energy.
Healing occurs as a result of both short-term and long-term rates of rest periods, and
depends on traffic rest periods, healing surface energy components, and the material properties
measured in compression creep or relaxation modulus tests. Because the HMAC mixture healing
properties are climatic dependent, fatigue healing calibration constants must be used to account
for the climatic location of a given HMAC pavement structure (67). In determining the final
field Nf, an anisotropic shift factor (discussed subsequently) is also introduced to account for the
anisotropic nature of HMAC.
The surface energies of the binder and aggregate in HMAC are made up of contributions
from nonpolar short-range Lifshitz-van der Waals forces and longer-range polar acid-base forces
mainly associated with hydrogen bonding (68, 70-71).
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62
The polar acid-base surface energy is itself also a combination of the acid surface energy
and the base surface energy. These polar forces typical of hydrogen bonding take longer to form
and act perpendicular to the crack faces to actively pull them together, while the nonpolar tensile
short-range and short-lived Lifshitz-van der Waals forces act in the plane of the crack face to
form a contractile skin that resists healing (44-45, 68, 70-71).
The difference between the total fracture and healing surface energies lies in the
measurement of the individual surface energy components using carefully selected materials
with known surface energy component values. Fracture components are found when dewetting,
and healing components are determined when wetting (44-45, 68, 70-71).
Figure 5-2 is a schematic illustration of the CMSE design and analysis system. The figure
shows that if the predicted Nf is less the design traffic ESALs, possible options include the
following:
• modifying the pavement structure, materials, and reliability level; and/or
• changing the HMAC mix-design and/or material type;
• reducing the pavement design life; and/or
• allowing an increased risk of premature failure, i.e., reducing the reliability level.
In this CMSE approach, the design shear strain (Figure 5-2) computed within the HMAC
layer of the pavement structure for Np analysis constitutes the failure load-response parameter.
This critical design shear strain is determined at the edge of a loaded wheel-tire using either a
layered linear-elastic or visco-elastic model of material behavior characterization. The utilization
of calibration constants in modeling SFh, Ni, and Np constitutes the calibration part of the CMSE
approach. This calibration simulates the field mechanism of microcrack growth in the HMAC
layer thickness with respect to traffic loading and environmental conditions.
INPUT/OUTPUT DATA
Table 5-1 summarizes the general CMSE fatigue analysis input and the expected output
data. These parameters and their respective components are discussed in more detail in
subsequent sections.
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63
NO
CMSE FATIGUE ANALYSIS
Pavement structure
Pavement materials
Traffic
Environment
Reliability
Nf Prediction
HMAC mixture characterization properties (from lab test or existing data from catalog)
Calibration, healing, & regression constants
Paris’ Law coefficients
Microcrack length failure threshold value
Design shear strain
Temperature correction factors
Anisotropy and healing shift factors
HMAC mixture fatigue resistance
Reliability factor (Q)
Nf ≥ Q × Traffic
YES
Final Fatigue Design
Figure 5-2. The CMSE Fatigue Design and Analysis System.
Page 84
64
Table 5-1. Summary of CMSE Fatigue Analysis Input and Output Data.
Source Parameter
Laboratory test data (HMAC mixture testing of cylindrical specimens)
- Tensile stress & strain - Relaxation modulus (tension & compression) - Uniaxial repeated direct-tension test data (strain, stress, time,
& N) - Anisotropic data (vertical & lateral modulus) - Dynamic contact angle for binder surface energy (SE) - Vapor pressure and adsorbed gas mass for aggregate SE
Analysis of laboratory test data
- Tensile strength - Relaxation modulus master-curves (tension & compression) - Non-linearity correction factor - DPSE & slope of DPSE vs. Log N plot - SE (∆Gf & ∆Gh) for binder & aggregates - Healing indices - Healing calibration constants - Creep compliance - Shear modulus - Load pulse shape factor
Field conditions (design data)
- Pavement structure (layer thickness) - Pavement materials (elastic modulus & Poisson’s ratio) - Traffic (ESALs, axle load, & tire pressure) - Environment (temperature & moisture conditions.) - Field calibration coefficients - Temperature correction factor
Computer stress-strain analysis - Design shear strain (γ) @ edge of a loaded tire
Other Parameters
- Reliability level (i.e., 95%) - Crack density - Microcrack length - HMAC brittle-ductile failure characterization - Stress intensity factors - Regression constants - Shear coefficient
OUTPUT
- Paris’ Law fracture coefficients (A and n) - Shift factor due to anisotropy (SFa) - Shift factor due to healing (SFh) - Fatigue load cycles to crack initiation (Ni) - Fatigue load cycles to crack propagation (Np) - HMAC mixture fatigue resistance (Nf)
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65
LABORATORY TESTING
The required laboratory tests for the CMSE approach of HMAC mixture fatigue analysis
include tensile strength, relaxation modulus in both tension and compression, uniaxial repeated
direct-tension, and surface energy (45, 68-69, 71). These tests are described in this section. For
each of these tests, at least two replicate cylindrical specimens were tested per aging condition
per mixture type. The cylindrical HMAC specimen fabrication procedure, including the final
dimensions consistent with the SGC compaction protocol, is described in Chapter 3.
Tensile Strength Test
The tensile strength test was conducted to determine the HMAC mixture tensile strength
(σt), which is a required input parameter for CMSE Nf analysis.
Test Protocol
The tensile strength (TS) test protocol involves applying a continuous increasing tensile
load to a cylindrical HMAC specimen at a constant elongation (deformation) rate of 1.27
mm/min (0.05 in/min) till failure (break point). This test is destructive and took at most
2 minutes to complete the test. Figure 5-3 shows the loading configuration for and typical results
from the tensile strength test.
Deformat ion
Load
(P)
Pmax Load
Load
Figure 5-3. Loading Configuration for Tensile Strength Test.
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66
Test Conditions and Data Acquisition
The tensile strength test was conducted in an environmentally controlled chamber at a
test temperature of 20±0.5 °C (68±32.9 °F). Specimens were preconditioned to 20 °C (68 °F) for
a minimum period of 2 hrs. The temperature was monitored and controlled through a
thermocouple probe attached inside a dummy HMAC specimen also placed in the environmental
chamber. An MTS equipped with an automatic data measuring system applied the loading.
Loading data were measured via the MTS load cell, and deformations were recorded via three
LVDTs attached vertically to the sides of the specimen. During the test, load and axial
deformation data were captured electronically every 0.1 s. Two replicate specimens were tested
per aging condition per mixture type.
Mixture tensile strength (σt) was calculated simply as the maximum tensile load at break
divided by the specimen cross-sectional area as follows:
2max
rP
t πσ = (Equation 5-1)
where:
σt = Tensile strength (MPa)
Pmax = Maximum tensile load at break (MPa)
r = Radius of cylindrical specimen (mm)
Relaxation Modulus Test
The time-dependent elastic relaxation modulus (Ei), modulus relaxation rate (mi), and
temperature correction factor (aT) constitute input parameters for the CMSE fatigue analysis.
These material properties were determined from the relaxation modulus test (30).
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67
Test Protocol
Relaxation modulus (RM) is a strain-controlled test. The test involves applying a
constant axial strain to a cylindrical HMAC specimen either in tension or compression for a
given time period and then releasing the strain for another given time period, thereby allowing
the specimen to rest or relax (elastic recovery). The test loading configuration is shown in
Figure 5-4.
-200
0
200
0 200 400 600 800 1000 1200 1400
Time, s
Mic
rostr
ain
Tension
Compression
Load
Load
Figure 5-4 Loading Configuration for Relaxation Modulus Test.
As shown in Figure 5-4, the loading sequence consisted of a 200 tensile microstrain
sitting for a period of 60 s followed by a 600 s rest period and application of a 200 compression
microstrain for 60 s followed by another 600 s rest period (30). Researchers selected 200
microstrain because, for the HMAC mixtures considered in this project, prior trial testing with
microstrains above 200 proved to be destructive, while those below 200 were too small to
produce meaningful results. A 60 s strain loading time was considered adequate to prevent
irrecoverable damage while a 600 s rest period was considered adequate to allow for elastic
recovery. The time interval for the strain load application from 0 to +200 or -200 microstrain
was 0.6 s, and the input strain waveform was actually a trapezoidal shape. Thus, the total test
time for both the tensile and compressive loading cycle for a given test temperature, say 10 °C
(50 °F), was approximately 25 minutes.
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68
Test Conditions and Data Acquisition
The research team conducted RM testing in an environmentally controlled chamber at
three temperatures, 10, 20, and 30 °C (50, 68, and 86 °F), to facilitate development of a
time-dependent RM master-curve. This master-curve is a graphical representation of the HMAC
mixture properties as a function of temperature and loading time. Note that HMAC is sensitive to
temperature and time of loading.
The temperatures were monitored and controlled at a tolerance of ±0.5 °C (±32.9 °F)
through a thermocouple probe attached inside a dummy HMAC specimen also placed in the
environmental chamber. For each temperature-test sequence, the minimum specimen
conditioning time was 2 hrs. The MTS provided the loading while an automated data
measurement system captured the data (time, load, and deformation) electronically every 0.5 s.
Loading data were measured via the MTS load cell, and deformations were recorded via three
LVDTs attached vertically to the sides of the specimen. Three replicate specimens were tested
per aging condition per mixture type.
Figure 5-5 is an example of the output stress response from the relaxation modulus test at
a single test temperature of 10 °C (50 °F).
-250
0
250
0 200 400 600 800 1000 1200 1400
Time, s
Stre
ss, p
si
Figure 5-5. Example of Stress Response from RM Test at 10 °C (50 °F).
Page 89
69
Equation 5-2 was used to calculate the elastic relaxation modulus as a function of the
measured load (stress) and strain.
επεσ
2rP
E == (Equation 5-2)
where:
E = Elastic modulus (MPa)
P = Load (kN)
ε = Strain (mm/mm)
A time-reduced superposition logarithmic analysis of the elastic modulus data for each
test temperature to a reference temperature of 20 °C (68 °F) generates the required time-
dependent RM master-curve. This master-curve is represented in the form of a simple power law.
By the same logarithmic analysis, temperature correction factors (aT) are determined, where aT
has a value of 1.0 for the 20 °C (68 °F) reference temperature.
Uniaxial Repeated Direct-Tension Test
The time-dependent tensile stress (σ (t)) is an input parameter required to calculate the
rate of dissipation of PS energy (b) that is necessary to calculate Ni. This material property was
determined from the uniaxial repeated direct-tension test discussed subsequently.
Test Protocol
Like the RM test, the uniaxial repeated direct-tension (RDT) test was conducted in a
strain controlled mode (68). An axial direct tensile microstrain of 350 was applied repeatedly to a
cylindrical HMAC specimen at a frequency of 1 Hz for a total of 1000 load cycles. The input
strain waveform was haversine shaped.
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70
The actual loading time was 0.1 s with a 0.9 s rest period between load pulses. Thus, a
complete load cycle including the rest period was 1.0 s. Figure 5-6 shows the loading
configuration. The 0.9 s rest period allowed for HMAC relaxation between the load pulses and
prevented the buildup of undesirable residual stresses discussed subsequently. This rest period
can also promote a limited amount of healing.
Nu mber of Load Cycles
350
Mic rostrain
(1,000)Load
Load
Figure 5-6. Loading Configuration for the RDT Test.
The haversine-shaped input strain waveform is representative of the field load pulse
developed under moving wheel loads of commercial vehicles on interstate highways (68). A
relatively high input strain magnitude of 350 microstrain was selected because this value
(350 microstrain) was considered substantial enough to induce cumulative micro fatigue damage
(microcracking) within the HMAC specimen during the test. In this test, while micro fatigue
damage is desirable, an appropriate input strain level must be selected that will allow the test to
continue to an appreciable number of load cycles to capture sufficient data that will allow for
calculation of the b slope parameter needed in the CMSE analysis. For this project, testing was
terminated at 1000 load cycles, during which time sufficient data had been captured for DPSE
analysis and subsequent calculation of the constant b. A complete RDT test thus took about
20 minutes.
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71
Test Conditions and Data Acquisition
The haversine input strain waveform was supplied by the MTS, and axial deformations
were measured via three LVDTs. Data (time, load, and deformations) were captured
electronically every 0.005 s. The research team conducted the RDT test in an environmentally
controlled chamber at a test temperature of 30±0.5 °C (86±32.9 °F). The minimum conditioning
period for the specimens was 2 hrs. The temperature was monitored and controlled through a
thermocouple probe attached inside a dummy HMAC specimen also placed in the environmental
chamber.
Three replicate cylindrical HMAC specimens that had previously been subjected to a
series of RM tests at 10, 20, and 30 °C (50, 68, and 86 °F) were used for this test for each aging
condition and each mixture type. It should be noted that the RM test was assumed to be non-
destructive in this project. However, the RDT test is a destructive test since some microdamage
occurs within the HMAC specimen even though damage may not be physically visible.
Figure 5-7 is an example of the stress response from the uniaxial repeated direct-tension
test at 30 °C (86 °F). The measured stress (σ(t)), strain (ε(t)), and time (t) are the required input
parameters for CMSE fatigue analysis to calculate DPSE.
-250
0
250
500
0 1 2 3 4 5
Time, s
Stre
ss, p
si
Figure 5-7. Stress Response from RDT Testing at 30 °C (86 °F).
Page 92
72
Anisotropic Test
The modulus of HMAC is an important input parameter used in predicting HMAC
mixture fatigue properties. HMAC is not an isotropic material, and therefore, its mechanical
properties (i.e., elastic modulus) are directionally dependent (72-73). The objective of the
anisotropic test was thus to measure the variation of HMAC modulus measured from different
directions, vertical (Ez) and horizontal or lateral (Ex and Ey), which constitute input parameters
for CMSE fatigue analysis. Primarily, the research team conducted the anisotropic (AN) test to
determine the shift factor due to anisotropy (SFa) discussed in the subsequent sections of this
chapter.
Test Protocol
In this project, the research team conducted the AN test consistent with the HMAC
elastic-resilient modulus test, but with both axial and radial deformation measurements for Ez
and Ex determination, respectively (64). AN is a destructive stress-controlled test with a
sinusoidal-shaped input stress waveform. The test involved repeated application of a sinusoidal-
shaped stress magnitude of 690 kPa (100 psi) at a loading frequency of 1 Hz for a total of 200
load cycles without any rest period. Figure 5-8 shows the AN test loading configuration.
Figure 5-8. Loading Configuration for the AN Test
0 2 4 6 8 10 12
Time s)
Stre
ss
(200)
690 kPa (100 psi)
Load
Load
Axi
al d
efor
mat
ion
Radial deformation
Ez
Ex Ey
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73
An input stress magnitude of 690 kPa is simulative of a truck tire pressure on an in situ
field HMAC pavement structure. For this project, AN testing was terminated at 200 load cycles,
during which time sufficient data had been captured for moduli analysis. With a loading
frequency of 1 Hz, the total AN test time was at most 5 minutes. Although AN is a destructive
test, the 200 load cycles was in most cases not sufficient enough to cause visible damage to some
specimens.
For an AN test of this nature, it is always a normal practice to subject the test specimens
to lateral pressure confinement to simulate field triaxial stress state, particularly when testing
unbound granular materials (74-75). In this project, the AN test was conducted under
unconfined lateral pressure conditions. However, the AN analysis models were adjusted to the
lateral pressure confinement conditions to simulate the laboratory triaxial stress state. This
adjustment was achieved through trial testing of several HMAC specimens under both
unconfined and confined laboratory lateral (345 kPa) pressure conditions and then comparing the
moduli results. The moduli results measured without pressure confinement were then
adjusted/modified to match the moduli results under lateral pressure confinement conditions,
thus accounting for triaxial stress state conditions. Note that it is much more convenient, easier,
and practical to conduct the HMAC AN test under unconfined lateral pressure conditions.
Test Conditions and Data Acquisition
The sinusoidal input stress waveform was supplied by the MTS, while axial and radial
deformations were measured via three LVDTs. Two LDVTs attached vertically to the sides of
the specimen were used for axial measurements, and one LVDT attached radially around the
center of the specimen was used for radial deformation measurements, as shown in Figure 5-8.
Data (time, load, and deformations) were captured electronically every 0.02 s.
Like other HMAC mixture tests in this project, the research team conducted the AN test
in an environmentally controlled chamber at a test temperature of 20±0.5 °C (68±32.9 °F). The
minimum conditioning period for the specimens was 2 hrs. The temperature was monitored and
controlled through a thermocouple probe attached inside a dummy HMAC specimen also placed
in the environmental chamber. Three replicate specimens were tested per aging condition per
mixture type.
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74
Figure 5-9 is an example of the strain responses from the AN test at 20 °C (68 °F)
recorded for a period of 60 s. While the AN test gives both the elastic and plastic strain responses
as shown in Figure 5-9, the response component of interest that is critical to fatigue is the elastic
strain. By contrast, the plastic strain is critical to permanent deformation, which was beyond the
scope of this project.
0
100
200
300
0 10 20 30 40 50 60
Time (s)
Rad
ial m
icro
stra
in
Plastic
Elastic
0
400
800
1,200
0 10 20 30 40 50 60
Time (s)
Axia
l mic
rost
rain
Plastic
Elastic
Figure 5-9. Example of Strain Responses from AN Testing @ 20 °C (68 °F).
Page 95
75
From the measured AN test data, the elastic moduli were calculated as a function of the
applied load (stress) and elastic strain response, as expressed by Equations 5-3 and 5-4 below
(64, 74-75). For simplicity, HMAC was assumed to be laterally isotropic, and therefore, Ex was
considered equivalent to Ey in magnitude
zz
zz a
Eε
σ= (Equation 5-3)
x
zxyx aEE
ενσ
== (Equation 5-4)
where:
Ez = Elastic modulus in the vertical direction (MPa)
Ex = Elastic modulus in the lateral direction (MPa)
σz = Applied compressive axial stress (MPa)
εz,εx = Axial and radial deformation, respectively (mm/mm)
ν = Poisson’s ratio (ν≅ 0.33)
ax, az = Anisotropic adjustment factors that account for laboratory lateral pressure
confinement conditions (ax ≅ 1.15, az ≅ 0.75)
In this project, the mean ax and az values were determined to be 1.15 and 0.75,
respectively (for both mixtures), and these were the values used for moduli computations. The
determination of these ai adjustment factors is illustrated in Appendix B.
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76
Surface Energy Measurements for the Binder – The Wilhelmy Plate Test
The surface energy measurements for the binders in this project were completed using the
Wilhelmy plate method (68, 71). Compared to other methods such as the drop weight, Du Nouy
ring, pendant drop, Sessile drop, capillary rise, and maximum bubble pressure, the Wilhelmy
plate method is relatively simple and does not require complex corrections factors to the
measured data (68, 71).
The contact angle between binder and any liquid solvent can be measured using the
Wilhelmy plate method. This method is based on kinetic force equilibrium when a very thin plate
is immersed or withdrawn from a liquid solvent at a very slow constant speed, as illustrated in
Figure 5-10 (76).
Figure 5-10. Loading Configuration for the Wilhelmy Plate Method.
The dynamic contact angle between binder and a liquid solvent measured during the
immersing process is called the advancing contact angle, while the dynamic contact angle during
the withdrawal process is called the receding contact angle.
Liquid solvent
Asphalt
F
F Advancing
Receding
Liquid solvent
Page 97
77
The advancing contact angle, which is a wetting process, is associated with the healing
process, while the receding angle is associated with the fracture mechanism. The total surface
free energy and its components for binder are calculated from these advancing and receding
contact angles. The surface free energy calculated from the advancing contact angles is called the
surface free energy of wetting or healing, while the surface free energy computed from the
receding contact angle is called the surface free energy of dewetting or fracturing.
Test Protocol and Data Acquisition
To complete the Wilhelmy plate test, approximately 0.65 g of hot-liquid binder heated to
about 144 °C (291.2 °F) was coated onto glass plates 50 mm ( ≅2 inches) in length by 25 mm (≅1
inch) in width with a 0.15 mm (0.006 inches) thickness. By dipping the glass plate into a mass
of hot-liquid binder to a depth of about 15 mm (0.6 inches), a thin binder film of approximately 1
mm (0.039 inches) thickness was created on the glass plate after allowing the excess binder to
drain off (68, 71).
As shown in Figure 5-7, the actual test protocol involves an automatically controlled
cycle (s) of immersion and withdrawal (receding) processes of the binder coated glass plates
into a liquid solvent to a depth of about 5 mm (0.2 inches) at an approximate uncontrolled
ambient temperature of 20±2 °C (68±32.9 °F). The temperature is not tightly controlled in this
test because previous research has indicated that the measurable contact angle, and consequently
the surface free energy, are not very temperature sensitive (68, 71). The total test time for both
the immersion and withdrawal processes took approximately 15 minutes.
Prior to testing, the binder-coated glass plate must be vacuumed for about 12 hrs in a
diseccator to de-air the binder. Three test binder samples are required per test per three liquid
solvents, and thus a total of nine samples were used per aging condition (i.e., 0, 3, and 6 months).
Distilled water, formamide, and glycerol were the three selected liquid solvents used in
this project because of their relatively large surface energies, immiscibility with binder, and wide
range of surface energy components. Table 5-2 lists the surface energy components of these
three liquid solvents (distilled water, formamide, and glycerol) (68, 71).
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78
Table 5-2. Surface Energy Components of Water, Formamide, and Glycerol.
Surface Free Energy Components (ergs/cm2) (68, 71) Solvent
ΓLi ΓLiLW ΓLi
+ ΓLi- ΓLi
AB
Distilled water 72.60 21.60 25.50 25.50 51.00
Formamide 58.00 39.00 2.28 39.60 19.00
Glycerol 64.00 34.00 3.60 57.40 30.00
During the test, the loading force for the immersion and receding processes was provided
by an automatically controlled Dynamic Contact Analyzer (DCA) balance shown in Figure 5-11.
Data (dynamic contact angle) were measured and captured electronically via the WinDCA
software. Figure 5-12 is an example of the measured dynamic advancing and receding contact
angles at 20±2 °C (68±35.6 °F).
Figure 5-11. The DCA Force Balance and Computer Setup - Wilhelmy Plate Test.
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79
Receding angle = 59.75° (De wetting or fracturing process)
Advancing angle = 61.67° (W etting or healing process)
Figure 5-12. Example of the DCA Software Display (Advancing and Receding).
For clarity, the vertical axis title in Figure 5-10 is “mass” in mg with a scale of -100 to
200 mg, and the horizontal axis title is “position” in mm with a scale of 0 to 7 mm (0 to 0.28
inches).
Binder Surface Energy Calculations
Equation 5-3 is the force equilibrium equation resulting from the immersion (advancing)
or the withdrawal (receding) processes during the Wilhelmy plate test. Based on the Young-
Dupre theory and the assumption that binder equilibrium film pressure is zero, Equation 5-5
reduces to Equation 5-6 (71).
gVgVCosPF AirLLt ρρθ +−Γ=∆ (Equation 5-5)
( ) −++− ΓΓ+ΓΓ+ΓΓ=+Γiiii LiLi
LWL
LWiiL Cos 2221 θ (Equation 5-6)
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80
where:
F = Applied force (kN)
Pt = Perimeter of the binder coated glass plate (m)
θ = Dynamic contact angle between binder and the liquid solvent, degrees (°)
V = Volume of immersed section of glass plate (m3)
ρ = Density (subscript “L” for liquid solvent and “Air” for air) (g/cm3)
g = Acceleration due to gravity (m/s2)
Γ = Surface free energy (ergs/cm2)
The dynamic contact angle θ (°) is the measurable parameter, advancing (wetting) or
receding (dewetting). ΓLiLW, ΓLi
+, and ΓLi- are known surface free energy components of the
liquid solvent. Γi LW, Γ i+, and Γ i
- are the three unknown components of the binder surface
free energy from Lifshtz-van der Waals forces, Lewis base, and Lewis acid, respectively, that
need to be determined. Note that the advancing (wetting) and receding (dewetting) contact
angles are used for determining the surface energy due to healing and fracturing, respectively.
Mathematically, three liquid solvents of known surface free energies must be used to
solve Equation 5-6 for the three unknown parameters Γi LW, Γ i+, and Γ i
-. Algebraically,
Equation 5-6 can easily be transformed into a familiar matrix form of simple linear simultaneous
equations expressed by Equation 5-7 (71):
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
3
2
1
3
2
1
333231
232221
131211
YYY
xxx
aaaaaaaaa
(Equation 5-7)
i
i
i
i
i
i
L
Li
L
Li
L
LWL
i aaaΓ
Γ=
Γ
Γ=
Γ
Γ=
−+
2 ,2 ,2 321 (Equation 5-8)
+− Γ=Γ=Γ= iiLW
i xxx 321 , , (Equation 5-9)
( ) ii CosxY θ+= 1 (Equation 5-10)
Page 101
81
where:
aki = Known surface energy components of the three liquid solvents
(distilled water, formamide, and glycerol) (ergs/cm2) (Table 5-2)
xi = The unknown surface energy components (Γi LW, Γ i+, and Γ i
-) of the
binder that need to be determined (ergs/cm2)
Yi(x) = Known function of the measured contact angles of the binder in the three
liquid solvents (θWater, θFormamide, and θGlycerol)
The solution of Equation 5-10 provides the surface free energy components of the binder
required for the CMSE fatigue analysis.
Surface Energy Measurements for the Aggregate – The Universal Sorption Device
In this project, the research team used the Universal Sorption Device (USD) for the
surface energy measurements of aggregates. The USD method utilizes a vacuum gravimetric
static sorption technique that identifies gas adsorption characteristics of selected solvents with
known surface free energy to indirectly determine the surface energies of the aggregate.
Sorption methods are particularly suitable for aggregate surface energy measurements because of
their ability to accommodate the peculiarity of sample size, irregular shape, mineralogy, and
surface texture associated with the aggregates (71).
Test Protocol and Data Acquisition
The USD setup is comprised of a Rubotherm magnetic suspension balance system, a
computer system (with Messpro software), a temperature control unit, a high quality vacuum
unit, a vacuum regulator, pressure transducers, a solvent container, and a vacuum dissector. A
schematic of the main components of the USD setup is illustrated in Figure 5-13.
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82
Solvent vapor supply
Magnetic suspension
balancePressure control and measurement
Balance, reading, tare, calibration, zero point and measuring point
Tem
per a
ture
con
trol
Sample chamber
Figure 5-13. USD Setup.
A Mettler balance is securely established on a platform with the hang-down Rubotherm
magnetic suspension balance and sample chamber beneath it. This magnetic suspension balance
has the ability to measure a sample mass of up to 200 g to an accuracy of 10-5 g, which is
sufficient for precise measurement of mass increase due to gas adsorbed onto the aggregate
surface. The whole USD system is fully automated with about 8 to 10 predetermined pressure
set-points that automatically trigger when the captured balance readings reach equilibrium.
With this USD sorption method, an aggregate fraction between the No.4 and No.8 sieve
size is suspended in the sample chamber, in a special container. Essentially, the size of
aggregate tested is that which passes the No.4 (4.75 mm [0.19 inches]) sieve but is retained on
the No. 8 sieve (2.36 mm [0.09 inches]). Theoretically, the surface free energy of aggregate is
not affected by the size of the aggregate because size is accounted for during the SE calculation
process (71). However, this aggregate fraction size (No.4 < aggregate size < No. 8) used in the
USD test is dictated by the limitation of the sample chamber size and the desired aggregate
surface area for sufficient gas adsorption that is representative of all aggregate fractional sizes.
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83
During the USD test process, once the chamber is vacuumed, a solvent vapor is injected
into the aggregate system. A highly sensitive magnetic suspension balance is used to measure
the amount of solvent adsorbed on the surface of the aggregate. The vapor pressure at the
aggregate surface is measured at the same time. The surface energy of the aggregate is
calculated after measuring the adsorption of three different solvents with known specific surface
free energy components. In this project, three solvents: distilled water, n-Hexane, and Methyl
Propyl Ketone 74 (MPK) with surface free energy components listed in Table 5-3, were used
(71).
Table 5-3. Surface Energy Components of Water, n-hexane, and MPK.
Surface Free Energy Components (ergs/cm2) (68, 71) Solvent
ΓLi ΓLiLW ΓLi
+ ΓLi- ΓLi
AB
Distilled water 72.60 21.60 25.50 25.50 51.00
n-hexane 18.40 18.40 0.00 19.60 0.00
MPK 24.70 24.70 0.00 0.00 0.00
Like binder SE measurements, aggregate SE measurements are also insensitive to
temperature, so the research team conducted the USD test at uncontrolled ambient temperature of
approximately 25±2 °C (77±35.6 °F). The total test time for a complete test set with three
solvents is about 60 to 70 hrs. For each solvent, 50 g sample of aggregates were tested for 0
months aging condition only. Note that aggregates are by nature insensitive to aging and thus 3
and 6 months aging at 60 °C (140 °F) were not considered for the aggregate SE measurements.
Prior to testing, the aggregate sample must be thoroughly cleaned with distilled water and oven-
dried (at about 120 °C (248 °F) for at least 8 hrs) to remove any dusty particles and moisture that
might negatively impact the results.
Data (vapor pressure, adsorbed gas mass, and test time) were measured and captured
electronically via the Messpro software. Figure 5-14 is an example of a typical output obtained
from the USD adsorption test for n-hexane adsorption on limestone aggregate at 25 °C (77 °F).
Page 104
84
Hexane adsorbed onto colorado limestone
0
0.05
0.1
0.15
0.2
0.25
0 50 100 150 200 250 300 350
Time, (min)
Mas
s ad
sorb
ed, (
mg/
g)adsorption without bouyancy correction
"adsorption with bouyancy correction"
Figure 5-14. Example of Adsorption of n-Hexane onto Limestone under USD Testing.
Aggregate SE Calculations
Once the adsorbed solvent mass and vapor pressure on the aggregate surface have been
measured and the adsorption data corrected for solvent vapor buoyancy using the generalized
Pitzer correlation model, the specific surface area of the aggregate was then calculated using the
BET (Brunauer, Emmett, and Teller) model shown by Equation 5-11 (68, 71):
( ) cnPP
cnc
PPnP
mm
11
00
+⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
− (Equation 5-11)
where:
P = Vapor pressure (MPa)
P0 = Saturated vapor pressure of the solute (MPa)
n = Specific amount adsorbed on the surface of the absorbent (mg)
nm = Monolayer capacity of the adsorbed solute on the absorbent (mg)
c = Parameter theoretically related to the net molar enthalpy of adsorption
Page 105
85
For the type of isotherms associated with the pressure conditions in this USD test, mn can
be obtained from the slope and the intercept of the straight line that best fits the plot of P/n(P-Po)
versus P/Po. The specific surface area (A) of the aggregate can then be calculated through the
following equation:
α⎟⎟⎠
⎞⎜⎜⎝
⎛=
MNn
A om (Equation 5-12)
And for a hexagonal close-packing model;
3/2
091.1 ⎟⎟⎠
⎞⎜⎜⎝
⎛=
ρα
oNM
(Equation 5-13)
where:
α = Projected area of a single molecule (m2)
No = Avogadros’ number (6.02 ×1023)
M = Molecular weight (g)
ρ = Density of the adsorbed molecule in liquid at the adsorption conditions
(g/cm3)
The result from the BET equation is used to calculate the spreading pressure at saturation
vapor pressure (πe) for each solvent using Gibbs free energy Equation 5-14 (71):
∫=0
0
p
e dPPn
ARTπ (Equation 5-14)
where:
πe = Spreading pressure at saturation vapor pressure of the solvent (ergs/cm2)
R = Universal gas constant (83.14 cm3 bar/mol.K)
T = Absolute temperature (Kelvin, K) (K = 273 + °C)
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86
The work of adhesion of a liquid on a solid (WA) can be expressed in terms of the surface
energy of the liquid ( lΓ ) and the equilibrium spreading pressure of adsorbed vapor on the solid
surface (πe) as shown in Equations 5-15 and 5-16:
leaW Γ+= 2π (Equation 5-15)
+−−+ ΓΓ+ΓΓ+ΓΓ=Γ+ lslsLW
lLWse 2222π (Equation 5-16)
where:
subscript s = Solid (aggregate)
subscript l = Liquid (solvent)
From Equations 5-15 and 5-16, the surface energy components and the total surface
energy of the aggregate can be determined by employing Equations 5-17 through 5-20):
( )LW
l
leLWs Γ
Γ+=Γ
42 2π (Equation 5-17)
Equation 5-17 is used to calculate the LWsΓ of the surface for a non-polar solvent on the
surface of the solid (aggregate). For a known mono-polar basic liquid vapor (subscript m ) and a
known bipolar liquid vapor (subscriptb ), the +Γs and −Γs values were calculated using
Equations 5-18 and 5-19 as follows:
( )−
+
ΓΓΓ−Γ+
=Γlm
LWlm
LWslme
s 42
2π
(Equation 5-18)
( )+
−+−
ΓΓΓ−ΓΓ−Γ+
=Γlb
lbsLW
lbLWslbe
s 422
2π
(Equation 5-19)
Page 107
87
Finally, the total surface energy of the aggregate ( sΓ ) is calculated as expressed by
Equation 5-20:
−+ΓΓ+Γ=Γ 2LWss (Equation 5-20)
Note, however that the current USD test protocol is still under development, in particular
to improve its test time efficiency as well as a general review of the SE data analysis procedures
(77). Appendix B provides a summary of the current USD test protocol and SE analysis
procedure as utilized in this project.
FAILURE CRITERIA
For the CMSE approach, fatigue failure is defined as crack initiation and propagation
through the HMAC layer thickness. In this project, researchers selected a maximum microcrack
length of 7.5 mm (0.30 inches) as the failure threshold value for crack initiation. This 7.5 mm
(0.30 inches) threshold value was selected based on Lytton et al.’s findings in their extensive
fatigue tests that crack propagation in the HMAC layer begins when microcracks grow and
coalesce to form a small crack of approximately 7.5 mm (0.30 inches) long (45).
ANALYSIS PROCEDURE
Equation 5-21, which relates field fatigue life (Nf) to the number of load cycles to crack
initiation (Ni) and crack propagation (Np) as a function of shift factors (SFi), is the fundamental
principle of the CMSE approach for fatigue modeling of HMAC mixtures (45).
( )piif NNSFN += (Equation 5-21)
where:
Nf = Fatigue life or number of load cycles to fatigue failure
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88
SFi = Product of the shift factors including HMAC anisotropy (SFa),
healing (SFh), aging (SFag), residual stresses (SFrs), stress state (SFss),
resilient dilation (SFd), and traffic wander ( SFtw).
Ni = Number of load cycles to crack initiation
Np = Number of load cycles to crack propagation
Each of these terms in Equation 5-21 is discussed in the subsequent subsections. In
Equation 5-21, the sum (Ni + Np) constitutes the laboratory fatigue life and the product of the
shift factors (SFi) and the sum (Ni + Np) constitute the field fatigue life.
Shift Factor due to Anisotropic Effect, SFa
Anisotropy arises due to the fact that HMAC is not isotropic as often assumed. The
mixture stiffness (modulus) in the lateral (horizontal) direction is not equal to that in the vertical
direction due to the differences in the particle orientation during compaction/construction.
During construction, there is always a high compactive effort in the vertical direction relative to
other directions. So the HMAC behavior or response to loading and/or the environment is
different in different directions. Consequently, the HMAC anisotropy must be considered in
fatigue analysis. However, most laboratory test protocols measure only the vertical stiffness and
assume isotropic behavior.
In the CMSE analysis, SFa takes care of the anisotropic behavior of the HMAC mixture.
Equation 5-22 shows the elastic modular relationship between the vertical (Ez) and horizontal
(Ex) moduli used in this project. Ez and Ex are measurable parameters from the AN test (34).
75.1
⎟⎟⎠
⎞⎜⎜⎝
⎛=
x
za E
ESF (Equation 5-22)
where:
SFa = Shift factor due to anisotropy, ranging between 1 and 5
Ez = Elastic modulus in vertical direction (MPa)
Ex = Elastic modulus in lateral or horizontal direction (MPa)
Page 109
89
Generally, because of the vertical orientation of the compactive effort during field
construction or laboratory compaction, Ez is always greater than Ex on the order of magnitude of
about 1.5 times (78). For simplicity purposes, HMAC was assumed to be laterally isotropic, and
therefore, Ex was considered as being equivalent to Ey in magnitude.
Shift Factor due to Healing Effect, SFh
Due to traffic rest periods and temperature variations, the asphalt binder has a tendency to
heal (closure of fracture surfaces), which often results in improvement in the overall HMAC
mixture fatigue performance. The CMSE approach takes this into account and relates healing to
traffic rest periods and temperature by the following equations (45, 71):
6
51g
TSF
rh a
tgSF ⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆+= (Equation 5-23)
ESALs Traffic 8010536.31 6
kNP
t DLr
×=∆ (Equation 5-24)
( ) 65
gohag = (Equation 5-25)
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆⎟⎟⎠
⎞⎜⎜⎝
⎛ −+
−+=
TSF
sr
o
atC
hhh
hhhh
β
21
212
1
(Equation 5-26)
[ ] ⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
∆=
⎟⎟⎠
⎞⎜⎜⎝
⎛
cmc
LWh EG
Ch1
11 (Equation 5-27)
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆=
⎟⎟⎠
⎞⎜⎜⎝
⎛
3
1
22 CEGCh
cm
c
ABh (Equation 5-28)
Page 110
90
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛∆∆
=c
LWh
ABh
mC
GGCh 5
4β (Equation 5-29)
where:
SFh = Shift factor due to binder healing effects, ranging between 1 and 10
∆tr = Rest period between major traffic loads (s)
∆t = Loading time (s)
aTSF = Temperature shift factor for field conditions (~1.0)
Csr = Square rest period factor (~1.0 )
a, g5, g6 = Fatigue field calibration constants
h0, 21−h ,= Healing rates
hβ = Healing index, ranging between 0 and 1.0
PDL = Pavement design life in years
80kN Traffic ESALs = Number of equivalent single axle loads over a given
pavement design period (e.g., 5 million over a 20-year design period)
C1-5 = Healing constants
Ec = Elastic relaxation modulus from compression RM master-curve (MPa)
mc = Exponent from compression RM master-curve
∆GhAB, ∆Gh
LW = Surface energies due to healing or dewetting (ergs/cm2)
In Equation 5-23, ∆tr represents the field long-term rest period and depends on the
pavement design life and traffic expressed in terms of traffic ESALs (45). The numerical value
of 31.536 × 106 in Equation 5-24 represents the total time in seconds for a 365 day calendar
year. The parameter aTSF is a temperature shift factor used to correct for temperature differences
between laboratory and field conditions. For simplicity, the research team used an aTSF value of
1.0, but this value can vary depending on the laboratory and field temperature conditions under
consideration. Csr represents the shape of the input strain wave rest period during the RDT test.
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91
As discussed previously, the periodic time interval between the input strain waveforms
for the RDT test in this project simulated a square-shaped form, with a total duration of 0.9 s.
This 0.9 s periodic time interval was considered as the square shaped rest period, so a Csr value
of 1.0 was used in the analysis (79). As stated previously, this rest period allowed for HMAC
relaxation, healing, and prevented the buildup of undesirable residual stresses during RDT
testing.
The parameters a, g5, g6 , h0, and 21−h are fatigue field calibration constants and healing
rates quantifying the HMAC mixture healing properties as a function of climatic location of the
pavement structure in question, SE due to healing, and HMAC mixture properties (Ec and mc)
obtained from compression relaxation modulus tests. These calibration constants and healing
rates also represent the HMAC mixture short-term rest periods and asphalt binder healing rates,
both short-term and long-term, respectively (45). The parameter hβ is a healing index ranging
between 0 and 1.0 that represents the maximum degree of healing achievable by the asphalt
binder (71).
The fatigue calibration coefficients g5 and g6 are climatic dependent. In this project, the
research team used values shown in Table 5-4, assuming Wet-No-Freeze and Dry-No-Freeze
climates. Table 5-5 provides an additional set of gi values based on accelerated laboratory
testing. These values in Tables 5-4 and 5-5 were established by Lytton et al. (45) in their
extensive field calibration study of fatigue cracking through Falling Weight Deflectometer
(FWD) tests in the field and accelerated laboratory tests. In their (Lytton et al.) findings, these
calibration coefficients provided a good fit between measured and predicted fatigue cracking
(45).
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92
Table 5-4. Fatigue Calibration Constants Based on Backcalculation of Asphalt Moduli from FWD Tests (Lytton et al. [45]).
Climatic Zone Coefficient
Wet-Freeze Wet-No-Freeze Dry-Freeze Dry-No-Freeze
g0 -2.090 -1.615 -2.121 -1.992
g1 1.952 1.980 1.707 1.984
g2 -6.108 -6.134 -5.907 -6.138
g3 0.154 0.160 0.162 1.540
g4 -2.111 -2.109 -2.048 -2.111
g5 0.037 0.097 0.056 0.051
g6 0.261 0.843 0.642 0.466
Table 5-5. Fatigue Calibration Constants Based on Laboratory Accelerated Tests (Lytton et al. [45]).
Climatic Zone Coefficient
Wet-Freeze Wet-No-Freeze Dry-Freeze Dry-No-Freeze
g0 -2.090 -1.429 -2.121 -2.024
g1 1.952 1.971 1.677 1.952
g2 -6.108 -6.174 -5.937 -6.107
g3 0.154 0.190 0.192 1.530
g4 -2.111 -2.079 -2.048 -2.113
g5 0.037 0.128 0.071 0.057
g6 0.261 1.075 0.762 0.492
SE and RM tests were discussed in previous sections of this chapter. ∆Gh Ec, and mc are
material (binder, aggregate, and HMAC mixture) dependent but also vary with the aging
condition of the binder and/or HMAC mixture, which has a net impact on SFh and Nf. As
discussed in Chapter 10, this preliminary study has shown that the variation of these parameters
(∆Gh, Ec, and mc) with 3 and 6 months aging of the binder and HMAC mixture at 60 °C (140 °F)
reduced the value of SFh considerably, particularly the resultant Nf. Analysis procedures for ∆Gh,
Ec, and mc are discussed subsequently.
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93
The healing constants C1 through C5 were backcalculated from regression analysis as a
function of the measured Ec, ∆Gh due to healing, and the healing rates (hi) using a spreadsheet
sum of square error (SSE) minimization technique (45, 68, 71).
Other Shift Factors
The shift factor due to aging (SFag) is discussed in Chapters 10 and 11 of this report. In
this current CMSE analysis, other shift factors including residual stress, stress state, dilation, and
traffic wander were not considered or were simply assigned a numerical value of 1.0 based on
the assumptions discussed in this section. In fact, the research team considered that some of these
factors are already included in the SFa and SFh shift factors. Nonetheless, future CMSE studies
should consider the possibility of exploring these shift factors in greater detail.
Residual Stresses, SFrs
In the field, because of incomplete elastic relaxation/recovery and short time intervals
between some traffic load applications (axles of the same vehicle), residual stresses can remain
in the pavement after the passage of each load cycle and may thus prestress the HMAC layer so
that the tensile stresses that occur with the next load cycle cause less, equivalent, or more
damage. If present, these residual stresses occur either in tension or compression depending
among other factors on the magnitude of the load and the pavement structure. On the same
principle, residual stresses can also buildup in laboratory test fatigue specimens particularly if
there is an insufficient rest period between load applications or if the specimens are not properly
loaded during the test. Equations 5-30 and 5-31 show the estimation of SFr according to Tseung
et al. (80):
( ) ⎟⎠⎞
⎜⎝⎛ −
−− ±=⎟⎟
⎠
⎞⎜⎜⎝
⎛±
= mmo
k
mo
r tPtP
SF2
11
1 21
(Equation 5-30)
)()(tEtP
t
ro ε
σ= (Equation 5-31)
Page 114
94
where:
Po = The percent of total strain remaining in the pavement as residual strain
after passage of the traffic load ( %)
t = Loading duration (s) (e.g., 0.1 s)
m = Stress relaxation rate (i.e., from tensile RM master-curve)
k21 = Laboratory determined constant as a function of m
σr(t) = Residual stresses (tensile or compressive) at time t (MPa)
εt = Total tensile strain (mm/mm)
E(t) = HMAC elastic modulus at time t (MPa)
Note that the expression k21 = 2/m may be valid only for HMAC subjected to uniaxial
strain-controlled loading tests. A different expression may be required for stress-controlled
loading tests.
According to Lytton et al. (45), SFr commonly ranges between 0.33 and 3.0 depending on
whether the residual stresses are tensile or compressive. In the absence of sufficient field data to
accurately predict the magnitude and/or determine whether these residual stresses (or strains)
will be tensile or compressive, and the fact that there was insignificant residual stress build-up in
the CMSE laboratory fatigue specimens under RDT testing (i.e., σr(t) ≈ Po ≈ 0.0), a SFr value of
1.0 was not an unreasonable assumption.
The RDT test in this project was conducted with a 0.9 s rest period between load pulses,
while the actual loading time was 0.1 s. The RDT out put stress response indicated that this 0.9 s
rest period sufficiently allowed for HMAC relaxation and subsequent prevention of residual
stress buildup. In fact, Equations 5-30 and 5-31 also show that if there are no residual stresses
(σr(t) ≈ 0.0), as in the case of the RDT test in this project, Po will be 0.0, and SFr will have a
numerical value of 1.0.
Note also that the CMSE fatigue analysis approach in this project assumes that there are
no residual stresses due to construction compaction in the field or SGC compaction in the
laboratory.
Page 115
95
Stress State, SFss
In a pavement structure under traffic loading, a triaxial stress state exists. The continuum
nature of the pavement material tends to transfer the applied stress in all three coordinate
directions (x, y, and z) based on the Poisson’s ratio and the interlayer bonding conditions. In the
laboratory, the stress state can be uniaxial, biaxial, or triaxial depending on the test protocol. A
shift factor is thus required to account for this difference in stress state between laboratory and
field conditions.
In a linear elastic stress-strain analysis, Al-Qadi et al. found that a shift factor based on
strain energy that accounts for the differences between laboratory and field pavement stress state
can vary approximately between 1.0 and 6.0 (81). Among others, this stress state depends on
materials, pavement structure, mode of loading (uniaxial, biaxial, or triaxial), and magnitude of
loading. With sufficient laboratory and field data, Al-Qadi et al. proposed that SFss can be
approximated by Equation 5-32 as follows (81):
( )
( )∑
∑
=
=
+
+== y
xizzii
y
xizzii
Field
Labss
EE
EE
WW
SF2
2
σε
σε (Equation 5-32)
where:
WLab = Total work done by laboratory loading ≅ strain energy (J/m3)
WField = Total work done by traffic loading in the field ≅ strain energy (J/m3)
σ, E, ε = stress (MPa), elastic modulus (MPa), and strain (mm/mm)
i = Subscript i, for x, y, and z coordinate directions
However, for the current CMSE analysis, the research team considered that the existence
of stress state (uniaxial, biaxial or triaxial) under laboratory and/or field loading conditions is
directly tied to the anisotropic response of HMAC. For example, the response behavior of
HMAC in terms of the elastic modulus under loading is directionally dependent, which is a
function of the stress state. Therefore, the effect of the stress state was considered to be indirectly
incorporated in the SFa factor.
Page 116
96
Resilient Dilation, SFd
Consistent with the theoretical definition of ν, resilient dilation will occur only for ν
values greater than 0.5. For pavement material subjected to vertical loading, dilation occurs when
the lateral deformation is greater than the vertical deformation, often as a result of inadequate
lateral confinement or support. This tendency to dilate is generally caused by the motion of
particles that tend to roll over one another (45).
Dilation is often very critical in unbound granular materials and the subgrade and can
often have a very significant impact on the overall fatigue performance of the pavement structure
in terms of stress-strain response. HMAC, on the other hand, is a bound material and is not very
sensitive to dilation. However, its stress-strain response to traffic loading and overall
performance can be greatly affected if the underlying pavement layers have potential to dilate.
SFd often ranges between 1.0 and 5.0 depending upon how much larger the Poisson’s
ratio (ν) is greater than 0.5 (45). Since, in this project, all the values of ν used were less than 0.5
(Chapter 3), researchers assumed the minimum value of 1.0 for SFd.
Traffic Wander, SFtw
Controlled laboratory fatigue testing applies loading repetitively to the same exact
location on the specimen. However, traffic loading in the field does not constrain itself to the
same position in the wheelpath. Accordingly, SFtw is needed to account for the traffic wander
when modeling pavement response to loading.
Blab and Litzka (82) postulated that the vehicle positions within the wheelpaths follow a
Laplace distribution function. Al-Qadi et al. (81) assumed a normal distribution around the
wheelpath with a mean of zero and a standard deviation, σ. Based on transverse strain
measurement in the wheelpath, Al-Qadi et al. derived SFtw values ranging between 1.6 and 2.7
for a σ range of 0.5 to 1.0.
However, for a given infinitesimal point within the pavement structure (i.e., in the
HMAC layer), the research team theorizes that the net engineering effect of traffic wander is to
relax and/or rest that particular point, thus minimizing the effect of residual stresses (tensile or
compressive) while simultaneously promoting elastic recovery and subsequent healing.
Page 117
97
This stress relaxation or rest period occurs because of traffic wander, and subsequent
loading follows a different path from the preceding one. Based on this theory, it can be assumed
that the effect of traffic wander is indirectly tied to SFrs and SFh. Therefore, an independent SFtw
was not considered in the current CMSE approach.
Also, Al-Qadi et al.’s study seems to indicate that with the assumption of normal traffic
distribution in the wheelpath and a relatively small value of σ (i.e., σ < 0.5), a SFtw value of 1.0
can possibly be derived (59).
Number of Load Cycles to Crack Initiation, Ni
Ni is defined as the number of load cycles required to initiate and grow a microcrack to
7.5 mm (0.30 inches) in length in the HMAC layer. In the CMSE analysis, Ni is determined
according to the following equation as a function of crack density, specimen cross-sectional area,
Paris’ Law fracture coefficients, and the rate that damage accumulates as indicated by DPSE (29,
30, 34):
( )
( )nD
nc
n
i CbA
AC
N ⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦⎤
⎢⎣⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛=
+ π421max (Equation 5-33)
⎟⎟⎠
⎞⎜⎜⎝
⎛=
tmn 1 (Equation 5-34)
∫∆
⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦
⎤⎢⎣
⎡
+−
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∆=
t nnm
f
tm
it
dttwG
EDI
kABDtt
0
)1(11
)1(1
2 )(σ
(Equation 5-35)
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
ππ
t
t
t mmSin
ED
][11 (Equation 5-36)
Page 118
98
( )BDi n
I+
=1
2 (Equation 5-37)
( )ndttt
Sindttwt t nn ln1744.05042.0).(
0 0
2 −=⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦⎤
⎢⎣⎡∆
=∫ ∫∆ ∆ π (Equation 5-38)
where:
Cmax = Maximum microcrack length (mm) (i.e., 7.5 mm (0.30 inches))
A, n = Paris’ Law fracture coefficients
Ac = Specimen cross-sectional area (m2)
b = Rate of accumulation of dissipation of pseudo strain energy
CD = Crack density (m/m2)
mt = Exponent obtained from the tension RM master-curve
(slope of the log relaxation modulus versus log time graph)
D1 = Time-dependent creep compliance (MPa-2)
Et = Elastic modulus from tension RM master-curve (MPa)
k = Stress intensity factor (~0.33)
∆Gf = Surface energy due to fracture or dewetting (ergs/cm2)
σt = Maximum mixture tensile strength at break (kPa)
Ii = Dimensionless stress integral factor in crack failure zone,
ranging between 1 and 2
nBD = Dimensionless brittle-ductile factor, ranging between 0 and 1
∆t = Repeated loading time (s) (~0.01 s)
∫∆t
n dttw0
)( = Load pulse shape factor, ranging between 0 and 1
t = Time (s)
The parameter Cmax defines the CMSE failure criterion and the subsequent failure
threshold value discussed previously. The crack density (CD) and rate of accumulation of
dissipation of pseudo strain energy (b) are discussed in the subsequent subsections of this
chapter.
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99
The parameters A and n are Paris’ Law fracture coefficients for material fracture
properties, which quantifies the HMAC mixture’s susceptibility to fracturing under loading.
According to Paris’ Law and Schapery’s theory, the coefficient n can be defined simply as the
inverse of the stress (tensile) relaxation rate (mt) as expressed by Equation 5-34 (26, 68, 71). This
assumption is valid for linear visco-elastic HMAC materials under a constant strain-controlled
RDT test (68, 71). Paris’ Law fracture coefficient A (Equation 5-35), on the other hand, is a
function of many parameters including k, D1, Et, mt, nBD, ∆Gf, σt, Ii, and wn(t). Based on Equation
5-33, a small value of A is desirable in terms of HMAC mixture fatigue resistance. Numerical
analysis, however, indicated that this coefficient A is very sensitive to nBD and σt if other factors
are held constant.
The parameter k is a material coefficient relating the length of the fracture process zone
(∝) to strain energy and mixture tensile strength. While this k is a measurable parameter, a value
of 0.33 was used based on Lytton et al.’s work and the assumption that it (k ≅ 0.33) does not vary
significantly with microcrack length in the fracture process zone (45).
As expressed by Equation 5-36, the time-dependent creep compliance, D1, was
determined as a function of Et and mt. Although an exact value of D1 can be measured from
uniaxial creep tests, this less costly and simple approximation produces a reasonable value that is
sufficient for use in HMAC mixture characterization analysis.
The numerical integration of wn(t) (Equation 5-38) with respect to time (t) describes the
shape of the input load pulse as a function of material fracture coefficient n (Paris’ Law). This
integral exhibits a linear relationship with the Paris’ Law fracture coefficient A, evident from
Equation 5-26, and has a subsequent inverse relationship with Ni. For a haversine-shaped input
strain waveform for the RDT test, as in this project, the integral reduces to a simple linear form
shown in Equation 5-39 with n as the only variable. Note that material response to loading is not
only magnitude dependent but also depends on the shape of the applied load form. As discussed
previously, a haversine-shaped input load form is a close simulation of HMAC load-response
under a moving wheel load (45, 68). The parameters Et, mt, ∆Gf, and σt are discussed
subsequently.
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100
Ii is an elasticity factor due to the integration of the stresses near the microcrack tip over a
small region in the microcrack failure zone (45, 68, 71). This factor, Ii, quantifies the materials’
elasticity ranges between 1.0 and 2.0 for perfectly linear-elastic (brittle) and rigid-plastic
(ductile) materials, respectively (83). Generally, a lower value (i.e., more linear-elastic) of Ii is
indicative of high susceptibility to fatigue damage. As expressed by Equation 5-28, the research
team quantified Ii simply as a function of nBD in this project. This brittle-ductile factor nBD,
which ranges between 0.0 for perfectly plastic materials and 1.0 for brittle materials, is an age-
related adjustment factor that accounts for the brittleness and ductility state of the HMAC
mixture in terms of stress-strain response under loading. In this project, unaged HMAC
specimens were assumed to exhibit plastic behavior and were subsequently assigned an nBD
value of 0.0. All the aged HMAC specimens were assumed to exhibit a brittle-ductile behavior
lying somewhere between perfectly plastic and brittle behavior, and were thus assigned nBD
values of 0.5 and 0.75 for 3 and 6 months aging conditions, respectively.
Number of Load Cycles to Crack Propagation, Np
Np refers to the number of load cycles required to propagate a 7.5 mm (0.30 inch)
microcrack through the HMAC layer thickness. As expressed by Equation 5-39, Np is determined
as a function of the maximum microcrack length, HMAC layer thickness, shear modulus, Paris’
Law fracture coefficients, and a design shear strain (45, 68, 71).
( ) ( ) ( )[ ]( ) nnq
nn
n
p dC
nqSGrAdN ⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦⎤
⎢⎣⎡−
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−=
−⎟⎠⎞
⎜⎝⎛ −
γ11
12
1max
21
(Equation 5-39)
( )νν21
)1(−−
=S (Equation 5-40)
⎟⎟⎠
⎞⎜⎜⎝
⎛=
z
xzt E
GEG (Equation 5-41)
Page 121
101
where:
A, n = Paris’ Law fracture coefficients
r, q = Regression constants for stress intensity factor (~4.40, 1.18) (45)
S = Shear coefficient
G = Shear modulus (MPa)
Cmax = Maximum microcrack length (mm) (i.e., 7.5 mm (0.30 inches))
d = HMAC layer thickness (mm)
γ = Maximum design shear strain at tire edge (mm/mm)
ν = Poisson’s ratio
Gxz = Resilient shear modulus (MPa)
Et = Elastic modulus from tensile RM master-curve (MPa)
If the elastic modular ratio Gxz/Ez in Equation 5-41 is unknown, Equation 5-42 below can
be used to approximate G (79). Equation 5-42 is a simple shear-elastic modulus relationship
based on elastic theory.
( )ν+=
12tE
G (Equation 5-42)
The parameters A, n, and Cmax were discussed in the previous subsections, and γ is
discussed in the subsequent text. Like Ni, an inverse relationship exists between A and Np,
indicating that a small value of A is desired in terms of HMAC mixture fatigue resistance. The
failure load-response parameter γ also exhibits an inverse relationship with Np.
Unlike for Ni, d is introduced in Np because during the microcrack propagation process,
for fatigue failure to occur, a microcrack length of a defined threshold value must actually
propagate through the HMAC layer thickness. By contrast, the prediction relationship for Ni is a
fatigue model for microcrack initiation and is independent of the parameter d.
Parameters r and q are regression constants that are a function of the stress intensity
distribution in the vicinity of the microcrack tip. In this study, values of 4.40 and 1.18 were
used, respectively, based on Lytton et al.’s work through FEM analysis (45). S is a shear
coefficient, which as defined by Equation 5-40 is a function of the Poisson’s ratio.
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Surface Energies, ∆GhAB, ∆Gh
LW, and ∆Gf
To cause load-induced damage in the form of fatigue cracking, energy must be expended
and equally energy must be expended to close the fracture surfaces. Surface energy data thus
constitute input parameters for the healing, crack initiation, and propagation calculations in the
CMSE fatigue analysis (Equations 5-43 through 5-49). The respective equations for the SE data
analysis required for the CMSE approach based on adhesive mode of fracturing under dry
conditions are described in this subsection.
LWj
LWi
LWij
LWhG Γ+Γ+Γ−=∆ (Equation 5-43)
ABj
ABi
ABij
ABhG Γ+Γ+Γ−=∆ (Equation 5-44)
ABj
ABi
ABij
LWj
LWi
LWij
ABf
LWff GGG Γ+Γ+Γ−Γ+Γ+Γ−=∆+∆=∆ (Equation 5-45)
And;
( )2LWj
LWi
LWij Γ−Γ=Γ (Equation 5-46)
( )−+ΓΓ=Γ iiAB
i 2 (Equation 5-47)
( )( )−−−+ Γ−ΓΓ−Γ=Γ jijiAB
ij 2 (Equation 5-48)
( )−+ΓΓ=Γ jjABj 2 (Equation 5-49)
where:
Γ = Surface free energy of binder or aggregate (ergs/cm2)
i,j = Subscript “i” for binder (healing or fracture) and “j” for aggregate
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103
h,f = Subscript “h” for healing and “f” for fracture
LW = Superscript “LW” for Lifshitz-van der Waals component
AB = Superscript “AB” for Acid-Base component
+ = Superscript “+” for Lewis acid component of surface interaction
− = Superscript “−” for Lewis base component of surface interaction
Γij = Interfacial surface energy between binder and aggregate due to “LW” or
“AB” (superscripts) components (ergs/cm2)
∆G = Total surface free energy due to “h” or “f” (subscripts) for “LW” and/or
“AB” (superscripts) components (ergs/cm2)
Equations 5-43 through 5-47 are the nonpolar surface bond energy for healing, the polar
surface bond energy for healing, the interactive term for the nonpolar LW surface bond energy
component, and the polar surface energy component for binder, respectively. These equations
quantify the bond strength within the binder mastic and the binder-aggregate adhesion.
Equation 5-45 is the total bond strength energy for fracture, which is made up of the
Liftshitz-van der Waals nonpolar energy components and the acid-base polar energy
components. Equation 5-45 is also commonly known as the total bond strength or Gibbs free
energy of fracture for the binder (83).
According to Lytton et al., greater resistance to fracture, is provided by larger bond
strength (cohesive or adhesive), and a greater healing capacity is promoted by the smallest LW
bond strength and the largest AB bond strength (45). On this basis, the lower the value of ∆Gh,
the greater the potential to heal; the higher the value of ∆Gf,, the greater the resistance to fracture
for HMAC.
In the simplest fundamental theory of energy, if a relatively higher amount of energy is
required or must be expended to cause fracture damage (i.e., initiate and propagate a
microcrack through the HMAC layer), then the HMAC mixture is substantially resistant to
fracture. If, on the other hand, a higher amount of energy is required or must be expended to
repair the fracture damage (i.e., healing which is defined as the closure of fracture surfaces) that
occurred during the fracturing process, then the HMAC mixture has relatively less potential to
self heal.
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104
Relaxation Modulus, Ei, Exponent, mi, and Temperature Correction Factor, aT
The elastic relaxation modulus (Ei) and exponent (mi) were determined from RM
master-curves of log modulus (Ei) versus log time (t) obtained from tension and compression
RM test data at a reference temperature of 20 oC (68 °F) (68). From the RM master-curve, a
power function of relaxation modulus and loading time was generated as follows:
imiEtE −= ξ)( (Equation 5-50)
Tat
=ξ (Equation 5-51)
where:
E(t) = Elastic relaxation modulus (MPa)
Ei = Initial elastic modulus (MPa) @ ξ = 1.0 s
tension (Et) or compression (Ec)
ξ, t = Reduced and actual test time, respectively (s)
mi = Exponential stress relaxation rate (0 ≤ mi < 1)
i = Subscript “t” for tension and “c” for compression
Equation 5-50 is a simple power law relationship that is valid for most HMAC materials
at intermediate and/or long times of loading (68). The exponent mi refers to the rate of stress
relaxation.
The temperature correction factors (aT) were obtained through utilization of the SSE
regression optimization technique using the spreadsheet “Solver” function and the Arrhenius
time-temperature superposition model shown in Equation 5-52 (84). The reference temperature
was 20 °C (68 °F), and thus, the aT for 20 °C (68 °F) was 1.0.
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛−=
refaT TT
AaLog 11 (Equation 5-52)
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105
where:
Aa = Material constant that is a function of the activation energy (∆Ha) and
ideal gas constant (Rg) (i.e., Aa = ∆Ha/2.303Rg)
T = Test temperature in degrees Kelvin (K = 273 + °C)
Tref = Reference temperature of interest (°K) (Kref = 273 + 20 = 293)
A default Ca value of 13,631.28 for ∆Ha ≅ 261,000 J/mol and Rg ≅ 8.314 J/(mol.°K) is
often used. However, the constant Aa can also be obtained easily using the spreadsheet SSE
regression optimization analysis.
DPSE and Constant, b
Researchers determined the constant b from a combination of the RM test data (Et and mt)
in tension and the RDT test data. The constant b is defined as the rate of damage (energy
dissipation) due to repeated loading that primarily causes fracture at intermediate temperatures
(68, 85).
For any selected load cycle, the time-dependent linear visco-elastic stress (under
damaged or undamaged conditions) was calculated using the Boltzmann superposition
constitutive equation as a function of the RM and the RDT test data (68, 79, 85-86). A
temperature correction factor (aT) was also introduced into the constitutive equation to normalize
the calculated stress to a given reference temperature.
In this project, aT was obtained from RM analysis, and the selected reference temperature
was 20 °C (68 °F). This temperature is a realistic simulation of field service temperatures at
which HMAC is susceptible to fracture damage under traffic loading. The RDT test was
conducted at 30 °C (86 °F), and therefore, the calculated stress had to be normalized to 20 °C
(68 °F).
Secondly, pseudo strain for damaged conditions was calculated as a function of the
normalized calculated linear visco-elastic stress for damaged conditions, the reference modulus
(ER), and ψ(t) (68). In the analysis, calculated PS rather than physically measured strain is used
to characterize damage and healing to separate and eliminate the time-dependent visco-elastic
behavior of the HMAC material from real damage during the strain controlled RDT test (68).
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106
ER is the modulus of the undamaged material determined from the first load cycle of the
RDT test. Note that no significant fracture damage was considered to occur during the first
RDT load cycle. The ψ(t), which is a function of the calculated and measured stress at the first
load cycle in an assumed undamaged condition, is introduced primarily to account for any
non-linearity of the undamaged visco-elastic material.
Finally, DPSE was then calculated as a product of the measured stress and the calculated
PS for damaged conditions using the double meridian distance method (DMD) for traverse area
determination (68, 87). This DPSE is simply the area in the pseudo hysteresis loop of the
measured tensile stress versus the calculated pseudo strain plotted as shown in Figure 5-1. The
respective equations are:
( )∑= )()()( tttDPSE dm
dR σεψ (Equation 5-53)
R
dcd
R Et
t)(
)(σ
ε = (Equation 5-54)
)()(
)()1(
)1(
tt
t um
uc
σσ
=Ψ (Equation 5-55)
)()( tt um
uc σσ ≠ , )()( tt d
mdc σσ ≠ (Equation 5-56)
)()()( )...2()1()1( ttt dNc
dc
uc σσσ ≠= , )()()( )...2()1()1( ttt d
Nmdm
um σσσ ≠= (Equation 5-57)
( ) τττε
τσ dd
tEtt
c)()(
0
∂−= ∫ (Equation 5-58)
Equation 5-58 is the general uniaxial stress-strain relationship applicable to most linear
visco-elastic materials including HMAC (68, 85). For a haversine-shaped input strain waveform,
Equation 5-58 can be written in the simple approximate numerical-integration form shown in
Equation 5-59:
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107
( )[ ]( )∑+=
=
−+∞+ −+∆=
1
0111 )(
ik
k
mkikic ttEECt τσ (Equation 5-59)
Assuming E∞ is zero, and using Et and mt for undamaged conditions and aT from RM
analysis, Equation 5-59 reduces to Equation 5-60 shown below:
∑+=
=
−
++ ⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛ −∆=
1
0
11
)()(
ik
k
m
T
kitkic
t
att
ECt τσ (Equation 5-60[a])
∑+=
=
−
++ ⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛ −∆=
1
0
11
()(
ik
k
m
T
kiktic
t
att
CEt τσ (Equation 5-60[b])
where:
)()1( tucσ = Calculated time-dependent linear visco-elastic tensile stress in an assumed
undamaged condition at the first load cycle (kPa)
)(tdcσ = Calculated time-dependent linear visco-elastic tensile stress under
damaged conditions at any load cycle other than the first (kPa)
ti+1,tk = Present and previous time, respectively (s)
τ = Loading time history, e.g., 0.0 to 0.10 s at which strains were measured (s)
∆τ = Time increment (s) (e.g., 0.005 s)
E(t-τ) = Tensile relaxation modulus in assumed undamaged condition at time t-τ
(MPa)
ε(τ) = Measured strain at previous time,τ (mm/mm)
Ck = Mean slope of any segment of the haversine input strain waveform
)(tdRε = Calculated pseudo strain for damaged conditions (mm/mm)
ER = Reference modulus for assumed undamaged material calculated from the
first load cycle (MPa)
ψ(t) = Dimensionless non-linearity correction factor (NLCF)
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108
)()1( tumσ = Measured tensile stress for assumed undamaged condition at the first load
cycle (MPa)
)(tdmσ = Measured tensile stress for damaged conditions (kPa)
aT = Temperature correction factor (from relaxation modulus analysis)
DPSE = Dissipated pseudo strain energy (J/m3)
g = Acceleration due to gravity (m/s2)
For a haversine-shaped input strain waveform, both the measured and approximate
(calculated) stress should exhibit a shape form of the format shown in Figure 5-15.
0 0.02 0.04 0.06 0.08 0.1 0.12
Time, s
Stre
ss
Figure 5-15. Output Stress Shape Form from RDT Test.
DPSE for selected laboratory test load cycles (N) was then plotted against log N to
generate a linear function of the format shown in Equation 5-61. The constant b in Equation 5-61
also defined as the rate of change in DSPE during microcrack growth, is simply the slope of the
DPSE versus log N plot, which is the required input parameter for the CMSE fatigue analysis
(68).
( )NbLogaWR += (Equation 5-61)
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109
where:
WR = DPSE (J/m3)
a = Constant or DPSE at the first load cycle
b = Slope of WR-log N plot
N = Load cycle
A plot of DPSE versus log N should exhibit a simple linear graph of the format shown in
Figure 5-16.
WR = a + b Log N
Log N
WR (J
/m3 )
Figure 5-16. Example of WR – Log N Plot.
The constant b is inversely related to the HMAC mixture fatigue resistance. Generally, a
comparatively small value of b is indicative of a relatively low rate of accumulation of micro
fatigue damage and consequently high HMAC mixture fatigue resistance.
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110
Crack Density, CD
Crack density calculations were based on the cavitation analysis by Marek and Herrin
(88) assuming a brittle mode of crack failure for the HMAC specimen (Figure 5-17). In their
analysis, Marek and Herrin used an average microcrack length of 0.381 mm (0.015 inches) based
on 281 HMAC specimens (88). Using these data, the research team calculated microcrack
density as a function of the number of cracks per specimen cross-sectional area to be 2.317 mm-2
(1495 in-2). This is the crack density value (2.317 mm-2 (1495 in-2)) used for the CMSE fatigue
analysis in this project.
Areas indicating brittle crack failure
Figure 5-17. Brittle Crack Failure Mode (Marek and Herrin [88]).
Shear Strain, γ
FEM analysis software that takes into account the visco-elastic nature of HMAC is
desirable for pavement stress-strain analysis to determine the maximum design shear strain γ at
the edge of a loaded tire. If a linear elastic analysis software such as ELSYM5 (62) is used, an
adjustment to the calculated γ must be done to account for the visco-elastic nature of HMAC. In
this project, the research team adjusted the computed linear elastic γ consistent with the FEM
adjustment criteria discussed in Chapter 3.
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111
Input parameters for the stress-strain analysis include traffic loading (ESALs and the axle
and tire configuration), pavement structure and material properties defined as a function of
environment (temperature and subgrade moisture conditions), and desired response locations. If
linear-elastic conditions are assumed, Equation 5-62 can be used to calculate γ (79).
SGpσ
γ = (Equation 5-62)
where:
σp = Tire pressure (kPa) (~690 kPa ≅ 100 psi)
S = Shear coefficient
G = Shear modulus (MPa)
VARIABILITY, STATISTICAL ANALYSIS, AND Nf PREDICTION
A COV was utilized as an estimate of the variability of Ln Nf predicted by the CMSE
approach. The COV expresses the standard deviation as a percent of the mean as follows:
xsCOV 100
= (Equation 5-63)
where:
COV = Coefficient of variation
s = Sample standard deviation
x = Sample mean, calculated based on replicate measurements of Nf
The COV is basically a measure of relative variation, and it says that the measurements
lie, on the average, within approximately COV percent of the mean (20). Replicate Nf predictions
obtained by varying the material input parameters based on actual laboratory measured replicate
values also provided a reasonable measure of variability and precision of the CMSE approach.
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112
For this CMSE approach, mean Ln Nf values were predicted from laboratory measured
material properties (i.e., tensile strength [σt]) on at least two replicate specimens. For this
analysis, a typical spreadsheet descriptive statistics tool, supplemented by a one-sample t-test,
was utilized. A 95 percent confidence/prediction interval (CI) for the mean Ln Nf was then
computed as expressed by Equation 5-63 (with a one-sample t-test for an assumed t-value of
zero) under the normality assumption on the distribution of Ln Nf .
⎥⎦
⎤⎢⎣
⎡±=
− nstxN
nf 2,2
CI %95 α (Equation 5-63)
where:
CI = Confidence interval
x = Mean Ln Nf value
s = Standard deviation of Ln Nf
α = Level of significance, i.e., 0.05 for 95% reliability level
n = Number of replicate specimens/measurements
SUMMARY
The following bullets summarize the CMSE fatigue analysis approach as utilized in this
project:
• The CMSE approach was formulated on the fundamental concepts of continuum
micromechanics and energy theory. This approach utilizes the fundamental HMAC mixture
properties including tensile strength, fracture, healing, visco-elasticity, anisotropy, crack
initiation, and crack propagation to estimate Nf. The energy theory in this CMSE approach is
conceptualized on the basis that energy must be expended to cause load-induced damage in
the form of cracking (fracture), and equally, energy must be expended to close up these
fracture surfaces, a process called healing.
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113
• The computation of the critical design shear strain at the edge of a loaded tire within a
representative field HMAC pavement structure for Np analysis constitutes the failure
load-response parameter for this approach. The utilization of field calibration constants in
modeling the healing process, Ni, and Np constitute the calibration part.
• For this CMSE approach, the HMAC material is characterized in terms of fracture and
healing processes and requires only relaxation tests in uniaxial tension and compression,
tensile strength tests, repeated load tests in uniaxial tension, and a catalog of fracture and
healing surface energy components of asphalt binders and aggregates measured separately.
• HMAC mixture characterization by CMSE laboratory testing utilizes gyratory compacted
cylindrical specimens under strain and temperature controlled conditions.
• Fatigue failure according to the CMSE approach in this project was defined as the number of
repetitive load cycles that are required to initiate and propagate a 7.5 mm (0.30 inches)
microcrack through the HMAC layer thickness.
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115
CHAPTER 6 THE CALIBRATED MECHANISTIC APPROACH
WITHOUT SURFACE ENERGY
The calibrated mechanistic approach without surface energy measurements follows the
same analysis concept and failure criteria as the CMSE approach except for a few differences.
Laboratory testing differences include the absence of SE measurements and RM testing in
compression. The analysis is slightly different to account for the fact that some of the input data
(i.e., SE and RM in compression) are not measured. Figure 6-1 and Table 6-1 summarize the CM
fatigue design and analysis system and input/output data.
The fundamental concepts, failure criteria, statistical analysis, and Nf prediction are
similar to the CMSE approach (Chapter 5) and are therefore not discussed in detail again in this
chapter.
Page 136
116
NO
CM FATIGUE ANALYSIS
Pavement structure
Pavement materials
Traffic
Environment
Reliability
Nf Prediction
HMAC material characterization properties (from lab test or existing data from catalog)
Calibration, healing, & regression constants
Paris’ Law coefficients
Microcrack length failure threshold value
Design shear strain
Temperature correction factors
Anisotropy and healing shift factors
HMAC mixture fatigue resistance
Reliability factor (Q)
Nf ≥ Q × Traffic
YES
Final Fatigue Design
Figure 6-1. The CM Fatigue Design and Analysis System.
Page 137
117
Table 6-1. Summary of CM Fatigue Analysis Input and Output Data.
Source Parameter
Laboratory test data (HMAC mixture testing of cylindrical specimens)
- Tensile stress & strain - Relaxation modulus (tension) - Uniaxial repeated direct-tension test data (strain, stress, time,
& N) - Anisotropic data (vertical & lateral modulus)
Analysis of laboratory test data
- Tensile strength - Relaxation modulus master-curves (tension & compression) - Non-linearity correction factor - DPSE & slope of DPSE vs. Log N plot - Healing indices - Healing calibration constants - Creep compliance - Shear modulus - Load pulse shape factor
Field conditions (design data)
- Pavement structure (i.e., layer thickness) - Pavement materials (i.e.,elastic modulus & Poisson’s ratio) - Traffic (i.e., ESALs, axle load, & tire pressure) - Environment (i.e., temperature & moisture conditions) - Field calibration coefficients - Temperature correction factor
Computer stress-strain analysis - Design shear strain (γ) @ edge of a loaded tire
Others
- Reliability level (i.e., 95%) - Crack density - Microcrack length - HMAC brittle-ductile failure characterization - Stress intensity factors - Regression constants - Shear coefficient
OUTPUT
- Paris’ Law coefficients of fracture (A, n) - Shift factor due to anisotropy (SFa) - Shift factor due to healing (SFh) - Fatigue load cycles to crack initiation (Ni) - Fatigue load cycles to crack propagation (Np) - HMAC mixture fatigue resistance (Nf)
Page 138
118
LABORATORY TESTING
Unlike the CMSE approach, SE measurements (for both binders and aggregates) and
mixture RM tests in compression are not required in the CM approach. However, all other test
protocols are similar to that of the CMSE approach.
SE Measurements for Binders and Aggregates
The complete CMSE analysis procedure involves the determination of the surface
energies of both binder and aggregate. The required SE input parameters for Nf prediction in the
CMSE approach are used to calculate ∆Gf and ∆Gh. Determination of the SE components
required for determining these inputs (∆Gf and ∆Gh) is a time-consuming process, with the
current SE test protocol (the Wilhelmy Plate and USD) requiring approximately 70 hrs to
complete (Chapter 5).
Therefore, in order to improve the practicality of the CMSE approach, Nf were predicted
using the CM procedure without using SE (∆Gf and ∆Gh) as an input parameter. Consequently,
no SE measurements are required in this CM approach.
RM Test in Compression
Mixture RM data in compression are required in the CMSE approach primarily to
compute the SFh. As discussed in the subsequent section, SFh computation in the CM procedure
does not require RM data in compression (i.e., E1c and mc) as input parameters.
ANALYSIS PROCEDURE
In terms of analysis, the major difference between the CMSE and CM approaches is in
the computation of SFh and Paris’ Law fracture coefficients A and n. These differences are
illustrated subsequently.
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119
Shift Factor Due to Healing, SFh
Equation 6-1 expresses the computation of SFh in the CM approach.
6
51g
TSF
rh a
tgSF ⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆+= (Equation 6-1)
ESALs Traffic 8010536.31 6
kNP
t DLr
×=∆ (Equation 6-2)
where:
∆tr = Rest period between major traffic loads (s)
aTSF = Temperature shift factor for field conditions ( ≅1.0)
gi = Fatigue field calibration constants
PDL = Pavement design life (i.e., 20 years)
It is clear that unlike the CMSE approach, ∆Gf, E1c, and mc are not required as input
parameters for the computation of SFh in this CM approach.
Paris’ Law Fracture Coefficients, A and n
The modified and CMSE calibrated empirical Equations 6-3 and 6-4 based on Lytton et
al.’s work show the computation of Paris’ Law fracture coefficients A and n, respectively,
according to the CM approach (45).
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
to m
ggn 1 (Equation 6-3)
( )⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
+⎟⎟⎠
⎞⎜⎜⎝
⎛++
=t
ttg
EmmSin
mg
g
Aσ
ππ log)(log1 4
32
10 (Equation 6-4)
Page 140
120
where:
A, n = Paris’ Law fracture coefficients
gi = Fatigue field calibration constants
mt = Stress relaxation rate from the tension RM master-curve
Et = Elastic modulus from tension RM master-curve (MPa)
σt = Mixture maximum tensile strength at break (kPa)
Fracture coefficients A and n are required as inputs for the determination of Ni and Np,
and subsequently Nf. The fatigue calibration coefficients gi are climatic dependent values that
were established by Lytton et al. (45) and shown in Table 5-4 in Chapter 5.
Note that empirical Equations 6-1 through 6-4 in this project were calibrated to the
CMSE approach by comparing the actual calculated numerical values to the corresponding
values obtained via the CMSE approach. Equation 6-4, for instance, is the modification of Lytton
et al.’s original Equation 6-5 (45).
( )⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
+⎟⎟⎠
⎞⎜⎜⎝
⎛+
=t
ttg
EmmSin
mg
g
Aσ
ππ log)(log 4
32
10 (Equation 6-5)
The A values computed using this empirical Equation 6-5 differed from the CMSE A
values by about 10 times (i.e., ACMSE ≅ 10 × ACM). Consequently, Equation 6-5 was modified as
shown in Equation 6-4 to match the CMSE results. However, more HMAC fatigue
characterization is required to further validate the simplified CM approach.
SUMMARY
The CM fatigue analysis approach, as utilized in this project, is summarized as follows:
• The CM approach follows the same concepts, failure criteria, and Nf prediction procedure as
the CMSE approach. The major differences stem from a reduced laboratory testing program
and resulting changes in the analysis procedure.
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• The CM does not require SE measurements (both binder and aggregates) and RM tests in
compression. Instead, these data inputs can be interpolated based on existing material
empirical relationships or obtained from existing catalogued data if desired.
• The SFh is computed primarily as a function of traffic rest periods, temperature shift factor,
fatigue calibration constants, pavement design life, and the design traffic ESALs. In contrast
to the CMSE approach, ∆Gf, E1c, and mc are not required as input parameters for the
computation of SFh in this CM approach.
• Paris’ Law fracture coefficients A and n are computed as a function of the material tensile
strength (σt), RM data in tension (E1t, mt), and fatigue field calibration constants (gi) using
empirically developed relationships that were calibrated to the CMSE approach.
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CHAPTER 7 THE PROPOSED NCHRP 1-37A 2002 PAVEMENT DESIGN GUIDE
This chapter summarizes the relevant aspects of the proposed NCHRP 1-37A 2002
Pavement Design Guide as utilized in this project. Further details can be found elsewhere
(3, 4, 89).
FUNDAMENTAL THEORY
The proposed NCHRP 1-37A 2002 Pavement Design Guide (M-E Pavement Design
Guide) adopts a ME approach for the structural design of HMAC pavements (3, 4, 89). There are
two major aspects of ME-based material characterization: pavement response properties and
major distress/transfer functions. Pavement response properties are required to predict states of
stress, strain, and displacement (deformation) within the pavement structure when subjected to
external wheel loads. These properties for assumed elastic material behavior are the elastic
modulus and Poisson’s ratio.
The major distress/transfer functions for HMAC pavements are load-related fatigue
fracture, permanent deformation, and thermal cracking. However, the focus of this project was
on fatigue characterization of HMAC mixtures, and therefore, only the fatigue analysis
component of the M-E Pavement Design Guide is discussed in this chapter. Figure 7-1 is a
schematic illustration of the fatigue design and analysis system for the M-E Pavement Design
Guide as utilized in this project.
Figure 7-1 shows that if the Nf prediction by the M-E Pavement Design Guide software in
terms of traffic ESALs is less than the actual design traffic ESALs, the following options are
feasible:
• reviewing/modifying the input data including the pavement structure, materials, traffic,
environment, reliability level, pavement design life, and analysis parameters (distress failure
limits);
• changing the HMAC mix-design and/or the material types; and
• changing the percentage crack failure criterion (i.e., 25 to 50 percent).
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Figure 7-1. The Fatigue Design and Analysis System for the M-E Pavement Design Guide
as Utilized in this Project.
Nf ≥ Design Traffic ESALS
YES
Final Fatigue Design
Nf Prediction
In terms of traffic ESALs for:
50% cracking in wheelpath
Binder & HMAC Mixture Characterization
Dynamic modulus testing
Binder DSR testing
Mixture volumetrics
NCHRP 1-37A PAVEMENT DESIGN GUIDE FATIGUE ANALYSIS
Pavement structure & materials
Traffic & environment
Reliability & design life
Analysis parameters
2002 Design Guide Software
Fatigue Analysis Model
Global Aging Model
Percent cracking in wheelpath
NO
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INPUT/OUTPUT DATA
The M-E Pavement Design Guide suggests a hierarchical system for materials
characterization. This system has three input levels. Level 1 represents a design philosophy of
the highest practically achievable reliability, and Levels 2 and 3 have successively lower
reliability. The Level 1 fatigue design procedure requires mixture volumetrics, dynamic modulus
(DM) values for HMAC mixture and a complex shear modulus for unaged binder as input
parameters. The binder data are used in the M-E Pavement Design Guide software to predict
mixture aging using the Global Aging Model (90). Field input data include traffic, pavement
structure, environment, and pavement design life. These input data requirements are summarized
in Table 7-1.
Table 7-1. Input/Output Data for the M-E Pavement Design Guide Software.
Source Parameter
Laboratory test data
- Dynamic modulus test data (i.e., temperature, frequency, & |E*| values)
- Binder DSR test data (i.e., temperature, G*, & δ values)
- Mixture volumetrics (i.e., binder content & AV)
Analysis of laboratory test data
- All calculations are software based
Field conditions (design data)
- Pavement structure (i.e., layer thickness) - Pavement materials (i.e., material type, elastic modulus,
Poisson’s ratio, gradations, and plasticity indices) - Traffic (i.e., AADT, axle load, & tire pressure) - Environment (i.e., climatic location) - Pavement design life (i.e., 20 years)
Computer stress-strain analysis
- All calculations are software based (utilized bottom-up crack failure mode in this project)
Other - Reliability level (i.e., 95%) - Analysis parameters (i.e., distress failure limits)
OUTPUT
- Percentage cracking in wheelpath - Nf in terms of traffic ESALs for 50% cracking in the
wheelpath - Assessment of adequate or inadequate performance
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For the output data in terms of fatigue cracking (alligator cracking), the software predicts
the percentage of fatigue cracking (along with other distresses) at any age of the pavement for a
given structure and traffic level under a particular environmental location. The failure criteria can
be set in two ways: setting the limit of percentage of cracks for a given number of traffic loads or
determining the number of traffic loads in terms of ESALS to reach a certain percentage of
cracks at a certain age of the pavement. In this project, the research team used the former
criteria.
The output data in this project thus consisted of percentage cracking in the wheelpath for
two input traffic levels of at least 2.5 and 5.0 million ESALs. Thereafter, Nf in terms of ESALs
was statistically determined for 50 percent cracking in the wheelpath.
LABORATORY TESTING
Characterization of the HMAC mixture and binder properties for Level 1 fatigue analysis
in the M-E Pavement Design Guide software requires the laboratory tests described in this
section.
Dynamic Shear Rheometer Test
Binder dynamic shear complex modulus (G*) and the phase angle (δ) required for
Level 1 fatigue analysis were measured using the standard DSR consistent with the AASHTO
test protocol designation TP5-98 (56). A minimum of two binder samples were tested, and test
results are shown in Table 2-1 (Chapter 2).
Dynamic Modulus Test
For Level 1 fatigue analysis, the M-E Pavement Design Guide software require the
dynamic modulus of the HMAC mixture measured over a range of temperatures and frequencies
using the dynamic modulus test. A typical DM test is performed over a range of different
temperatures by applying sinusoidal axial loading at different frequencies to an unconfined
specimen.
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Test Protocol
In this project, the DM test was conducted in accordance with the AASHTO designation:
TP 62-03 Standard Method of Test for Determining Dynamic Modulus of Hot Mix Asphalt
Concrete Mixtures at five test temperatures of -10, 4.4, 20, 38, and 54.4 °C (14, 40, 70, 100, and
130 °F) and six loading frequencies of 25, 10, 5, 1, 0.5, and 0.1 Hz (91).
DM is a stress-controlled test in compressive axial loading mode, and the test protocol in
this project involved applying a sinusoidal dynamic compressive-loading (stress) to gyratory
compacted cylindrical specimens of 150 mm (6 inches) in height by 100 mm (4 inches) in
diameter. Figure 7-2 shows the DM loading configuration.
Time (s)
Stre
ss
Load
Load
Figure 7-2. Loading Configuration for Dynamic Modulus Test.
The stress level for measuring the DM was chosen to maintain the measured resilient
strain (recoverable) within 50 to 150 microstrains, consistent with the TP 62-03 test protocol
(91). The order for conducting each test was from lowest to highest temperature and highest to
lowest frequency of loading at each temperature to minimize specimen damage. For each
temperature-frequency test sequence, the test terminates automatically when a preset number of
load cycles have been reached (91).
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Test Conditions and Data Acquisition
The sinusoidal axial stress waveform was supplied by the Universal Testing Machine
(UTM-25) shown in Figure 7-3. Axial deformations were measured via three LVDTs. The
research team conducted the DM test in an environmentally controlled chamber at test
temperatures of -10, 4.4, 20, 38, and 54.4 °C (14, 40, 70, 100, and 130 °F) for each specimen.
For each test temperature, the specimens were subjected to six consecutive loading frequencies
of 25, 10, 5, 1, 0.5, and 0.1 Hz.
Figure 7-3. The Universal Testing Machine.
The minimum conditioning period for the specimens for each test temperature was
2 hrs. This temperature was monitored and controlled through a thermocouple probe attached
inside a dummy HMAC specimen also placed in the environmental chamber. For each mixture
type, three replicate HMAC specimens were tested, but only for 0 months aging condition. Note
that the M-E Pavement Design Guide software encompasses a Global Aging Model that takes
into account binder aging in the fatigue analysis (90).
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During the DM tests, data (time, load, and deformations) were captured electronically
every 0.001 s. Figure 7-4 is an example of the compressive axial strain response from DM
testing at 4.4 °C (40 °F).
Figure 7-4. Compressive Axial Strain Response from DM Testing at 4.4 °C (40 °F).
The typical parameters, which result from DM testing, are the complex modulus (E*) and
the phase angle (δ). The E* is a function of the storage modulus (E′ ) and loss modulus (E″).
The magnitude of the E* is represented as shown in Equation 7-1.
0
0*εσ
=E (Equation 7-1)
δCosEE *' = (Equation 7-2)
δSinEE *"= (Equation 7-3)
where:
0σ = Axial stress (MPa)
0ε = Axial strain (mm/mm)
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However, the E* calculations were automatically done concurrently via the UTM-25
software during DM testing. Table 7-2 is an example of the output data from DM testing using
the UTM test setup. The E*, frequency, and temperature are actual input data to the M-E
Pavement Design Guide software.
Table 7-2. Example of Output Data from DM Testing at 4. 4 °C (40 °F).
Frequency (Hz) Parameter (summed average) 25 10 5 1 0.5 0.1
Dynamic modulus (|E*|)(MPa) 19,056 17,538 16,078 13,343 12,118 9,432Phase angle ( °) 5.24 8.31 9.84 13.15 14.95 18.99Dynamic stress (kPa) 1567.7 1713.6 1653.9 1683.0 1607.7 1505.6Recoverable axial microstrain 82.3 97.7 102.9 126.1 132.7 150.6Permanent axial microstrain 106.6 152.1 160.9 173.7 175.4 271.1
Temperature (°C) 4.4 4.4 4.4 4.4 4.4 4.4
For generating the E* master-curve as a function of loading time or frequency, the
following time-temperature superposition signomoidal model, as demonstrated by Pellinen et al.,
is often used and is in fact built in the M-E Pavement Design Guide software (92):
)log(1*)( ξγβ
αδ−+
+=e
ELog (Equation 7-4)
where:
E* = Complex modulus (MPa)
ξ = Reduced frequency (Hz)
δ = Minimum modulus value (MPa)
α = Span of modulus values
β = Shape parameter
γ = Shape parameter
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FAILURE CRITERIA
The fatigue failure criteria for the M-E Pavement Design Guide software in this project
was defined as the number of traffic ESALs required to cause 50 percent alligator cracking
(bottom-up) on a 152.4 m (500 ft) stretch of the wheelpath. This 50 percent threshold value is
consistent with the TxDOT tolerable limit based on the 2003 TxDOT PMIS report (61).
ANALYSIS PROCEDURE
The fatigue analysis procedure for the M-E Pavement Design Guide is a step-by-step
computerized process based on the modified Asphalt Institute predictive model incorporated in
the software (21, 89).
( ) ( ) 332211
kktff
ff EkN ββεβ −−= (Equation 7-5)
where:
Nf = Number of repetitions to fatigue cracking
εt = Tensile strain at the critical location of the HMAC layer
E = Stiffness of the HMAC mixture
βfi = Calibration parameters
ki = Laboratory regression coefficients
The βfi calibration parameters incorporate state/regional/national calibration coefficients.
In this project, default national calibration factors, which are inbuilt in the M-E Pavement Design
Guide software, were used. Regression coefficients ki are coefficients that relate to material
properties. E is the stiffness of the HMAC mixture, which the M-E Pavement Design Guide
software determines from the DM test data during that analysis. The horizontal tensile strain (εt)
constitutes the mechanistic failure load-response parameter and was computed at the bottom of
the HMAC layer in this project.
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As pointed out previously, the M-E Pavement Design Guide incorporates a Global Aging
Model that takes into account the effects of binder aging with time in the overall fatigue analysis
process (3, 4, 89, 90). The model is based on the change in binder viscosity as a function of
pavement age, AV, environment, traffic loading, and pavement depth to account for both short-
term aging that occurs during mixing and construction operations and long-term aging during
service. The output of the Global Aging Model (GAM) is basically a prediction of the binder
viscosity at any time and any depth in the pavement system, which is ultimately incorporated in
the overall fatigue analysis process.
VARIABILITY, STATISTICAL ANALYSIS, AND Nf PREDICTION
For traffic input levels of 2.5 and 5.0 million ESALs and for each mixture type in each
pavement structure and under each environmental condition, the research team predicted the
percentage cracking in the wheelpath for at least two HMAC specimens using the M-E Pavement
Design Guide software. Using these percentages, cracking output from the M-E Pavement
Design Guide software for these specimens, mean Nf values in terms of ESALs were statistically
predicted for 50 percent cracking. A 95 percent prediction interval was also determined using
the least squares line regression analysis.
SUMMARY
The bullets below summarize the fatigue analysis component of the M-E Pavement
Design Guide as utilized in this project:
• The M-E Pavement Design Guide adopts a ME approach for the structural design of HMAC
pavements. In terms of fatigue analysis, the M-E Pavement Design Guide software utilizes
the modified Shell Oil fatigue damage predictive equation with tensile strain as the primary
mechanistic failure load-response parameter associated with crack growth.
• The M-E Pavement Design Guide software incorporates binder aging effects analysis using a
Global Aging Model. It also incorporates comprehensive traffic and climatic analysis
models.
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• The Guide characterizes pavement materials in a three-level hierarchical system, with Level
1 representing the possible highest achievable reliability level.
• For Level 1 fatigue input analysis, HMAC mixture characterization through dynamic
modulus testing at five different temperatures and six loading frequencies utilizes gyratory
compacted cylindrical HMAC specimens. Other required material tests include mixture
volumetrics and binder DSR data.
• Fatigue failure for the M-E Pavement Design Guide software analysis was defined as the
number of applicable repetitive load cycles expressed in terms of traffic ESALs required to
cause 50 percent cracking in the wheelpath.
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CHAPTER 8 BINDER OXIDATIVE HARDENING BACKGROUND AND TESTING
METHODOLOGY
Binder oxidation is a major contributor to age-related pavement failure (93). Through
oxidation, the binder becomes stiffer and more brittle and thus less able to sustain, without
damage, the deformations of flexible pavements. This project investigated the role that this
binder embrittlement plays in the phenomenon of fatigue resistance.
This chapter includes further discussion of 1) binder oxidation and embrittlement in both
laboratory and pavement aging, 2) the objectives of binder measurements in understanding
pavement fatigue resistance, and 3) the experimental methodology used in this project to
evaluate binder aging and to relate it to HMAC mixture properties.
BINDER OXIDATION AND EMBRITTLEMENT (52, 93)
As briefly introduced above, binders experience hardening and embrittlement over time
that reduces the performance of flexible pavements. The process is relentless and thus, over
time, can destroy the pavement. The constancy of the hardening rate over time and the depth to
which oxidation occurs, based on recent pavement data, is surprising and at the same time
critical to understanding pavement durability for both unmodified and modified binders.
As binders oxidize, carbonyl (– C=O) groups are formed that increase the polarity of their
host compounds and make them much more likely to associate with other polar compounds. As
they form these associations, they create less soluble asphaltene materials, which behave like
solid particles. This composition change, taken far enough, results in orders-of-magnitude
increases in both the binder’s viscous and elastic stiffness properties. Thus the oxidized binder
sustains sheared stress with deformation (high elastic stiffness) and simultaneously the material
cannot relieve the stress by flow (high viscosity), resulting in a pavement that is very brittle and
susceptible to fatigue and thermal cracking.
The Maxwell model is a very simple way of explaining, in a qualitative sense, the
essence of the impact of this increase in both elastic stiffness and viscosity on elongational flow
of a binder. The model is that of an elastic spring in series with a viscous dashpot element, as
shown in Figure 8-1.
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Figure 8-1. The Maxwell Model.
The stress that builds in the combined element is the result of the balance between the
elastic modulus and the viscosity. Upon elongation at constant rate, the stress versus elongation
response rises in response to the elastic spring but then goes through a maximum value before
decaying over time in response to viscous flow. The value of the maximum stress depends upon
the relative values of the elastic modulus and the viscosity. The higher their values, the higher
the maximum stress; the lower the values, the lower the maximum stress. If the maximum stress
exceeds the failure stress of the material, then failure occurs.
This Maxwell model is very simple and certainly is too simple to quantitatively
characterize asphalt materials, but it still captures the basic elements that are important to
understanding binder failure that occurs due to oxidation and embrittlement. As asphalts
oxidize, they harden, a process that simultaneously increases its elastic stiffness and its viscosity.
Consequently, in the context of the Maxwell model, with aging and consequent hardening, a
binder cannot take as much deformation without building to a stress level that results in its
failure stress being exceeded. So, as binders age and harden, their ductilities decrease
dramatically. The binder ductility for a newly constructed pavement may be of the order of 30
cm (11.8 inches) (15 °C,1 cm/min) (59° F, 0.39 inches) where as the binder ductility of a
heavily aged pavement will be much lower, down to 3 cm (1.18 inches) or less.
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Literature reports emphasize the importance of a binder’s ductility to pavement
durability. Several studies report that a value of the 15 °C (59 °F) ductility at 1 cm/min (0.39
inches/min) in the range of 2 to 3 cm (0.79 to 1.18 inches) corresponds to a critical level for age-
related cracking in pavements (93, 94).
This embrittlement of binders has been captured with the discovery of a correlation
between binder ductility (measured at 15 °C, 1 cm/min) (59 °F, 0.39 inches/min) and binder
DSR properties (dynamic elastic shear modulus, G’ and dynamic viscosity, η’, equal to G”/ω)
shown in Figure 8-2. A very good correlation exists between binder ductility and G’/(η’/G’) (or,
equivalently G’/[G”/ωG’]), demonstrating the interplay between elastic stiffness and ability to
flow in determining binder brittleness, as discussed above in the context of the Maxwell model.
Figure 8-2. Correlation of Aged-Binder Ductility with the DSR Function G’/( η’/G’) for Unmodified Binders (52) (°F = 32 + 1.8(°C)).
This correlation is depicted on a “map” of G’ versus η’/G’ (Figure 8-3), which tracks a
pavement binder as it ages in service (94-96). This particular binder is from highway SH 21
between Bryan and Caldwell but represents the trends seen for all conventional binders.
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Figure 8-3. Binder Aging Path on a G’ versus η’/G’ Map (Pavement-aged Binders) (52)
(°F = 32 + 1.8(°C)).
On this type of plot, with increased aging, a binder moves, over time, from the lower
right toward the upper left as the result of increases in both the elastic stiffness and viscosity (but
note that G’ increases more than viscosity, i.e., G”/ω, because movement is toward the left with
smaller values of η’/G’. Note also the dashed lines that represent lines of constant ductility,
calculated from the correlation of Figure 8-2 below 10 cm (3.93 inches).
Recent evidence suggests that pavement binders age at surprisingly constant rates and to
surprising depths. Figure 8-3 illustrates this conclusion from Glover et al. contained in Research
Report 1872-2 (52), through measurements on highway SH 21 between Bryan and Caldwell; all
data shown in this figure are from a single station, #1277. This highway was constructed from
July 1986 to July1988 in three, 50 mm (2 inch) lifts. The solid symbols (with the exception of
the solid diamond) are binder measurements from cores taken from the third lift down from the
surface of the pavement, as originally constructed.
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With each lift being 50 mm (2 inches) thick, this bottom lift had 100 mm (4 inches) of
pavement material on top of it. (Note: In 2000, this pavement had a chip seal and overlay placed
on top of it, burying the original lifts even more.) Yet, even buried this deeply, its binder moves
across the DSR “map” in a relentless fashion and at about the same pace as the top lift (open
symbols). Binder from the 1989 bottom lift has an estimated ductility of 20 cm (7.87 inches) at
15 °C (59 °F). By 1996, it was reduced by aging to 5.6 cm (2.2 inches), and by 2002, it was less
than 5 cm (1.97 inches). Meanwhile, the top lift binder’s ductility was estimated to be 16 cm
(6.3 inches) in 1989, 4.5 cm (1.77 inches) in 1996, and about 4 cm (1.57 inches) in 2002. The
march across the DSR map was not that different for the top lift compared to the bottom lift.
Binder from the middle lift, taken in 1989 and 1992, is also shown and tracks well with the other
lifts. Note that the rolling thin-film oven test (RTFOT) plus pressure aging vessel laboratory-
aged binder matches the 1992 pavement-aged binder, suggesting that for this pavement, RTFOT
plus PAV is approximately equivalent to hot-mix and construction aging plus four years of field
pavement aging. These results are rather remarkable and strongly suggest, as noted above, that
oxidative aging rates are remarkably constant over time and, beyond the very top portion of the
pavement, proceed at remarkably uniform rates, at least to several inches below the surface of
the pavement.
Note that the literature reports that ductility values in the range of 2 to 3 cm (0.79 to 1.18
inches) for 15 °C (59 °F) at 1 cm/min (0.39 inches/min) appear to correspond to a critical level
for age-related cracking. Thus, the top-left corner of the pavement aging figure (Figure 8-3) is a
suspect region for pavement performance. While this region has not yet been verified
conclusively to be a critical zone, recent pavement data, including several long-term pavement
performance pavements, are consistent with this preliminary conclusion.
Clearly, binder properties change drastically over the life of a pavement. These changes
result in a dramatic decrease in flexibility and occur continuously throughout its service lifetime.
It is the objective of this project to investigate how these changes impact the fatigue resistance of
HMAC pavements. Ultimately, the objective is to predict reductions in pavement fatigue
resistance from laboratory measurements of binder oxidation and embrittlement.
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BINDERS STUDIED
Changes in binder properties with aging are to be related to changes in mixture properties
with the objective of learning how to predict changes in mixture (and ultimately pavement)
fatigue lives due to binder stiffening. To this end, a PG 64-22 unmodified binder was used in a
basic mixture (denoted as the Bryan Mixture), and a PG76-22 modified binder was used in a rut
resistant mixture (denoted as the Yoakum Mixture). These binders were tested in both aged and
unaged conditions. Chapters 3 through 7 discussed the aging and testing of HMAC mixtures. The
results from all of these tests are presented in Chapters 9 through 11.
Laboratory-Aged Binders
Two different methods of accelerated aging were used in this project. A stirred air flow
test (SAFT), which stimulates the hot mix process, was used for short-term aging comparisons
(97, 98). An environmental room at 60 °C (140 °F) and atmospheric pressure and 50 percent
relative humidity was used for long-term aging comparisons. Aging at 60 °C (140 °F) is used as
an approximation to field aging.
Neat (original) binder was aged by both of these means and subsequently tested; binder in
compacted mixes was aged in the 60 °C (140 °F) environmental temperature-controlled room
and had to be extracted and recovered before testing.
Binders Recovered from HMAC Mixtures
An effective extraction and recovery process is necessary to compare the properties of
mix-aged binder with those of the original binder. The process used in this project consisted of
two parts: 1) the extraction process, and 2) the filtration and recovery process.
At a mixture binder content of about 5 percent of total mass, approximately 150 g of
HMAC mixture were needed to obtain approximately 7 g of binder. The mixtures were broken
into small pieces with a hammer before extracting the binder from the HMAC specimens.
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Toluene and ethanol were used for the binder extraction process. A total of three
successive washes were used in the extraction process. For the first wash, 100 mL of toluene
was used to extract binder from the aggregate by contact for 20 minutes. The second and third
washes, also for 20 minutes each, used a 15 percent weight ethanol-toluene solution. The washes
were filtered two times using a new doubled coffee filter each time. The filtered solution was
then distributed among six 15 mL conical type tubes (approximately 12 mL solution per tube)
and centrifuged at about 3000 rpm for 10 minutes to remove aggregate from the solution.
The binder was recovered from the solvent with a Buchi, RE 111 rotovap. During
removal of the solvent, the bath temperature was kept at 100 oC (212 °F) to avoid hardening or
softening of the asphalt in dilute solution. When no more solvent could be detected visually
dripping from the condenser, the temperature was increased to 173.9 oC (345 °F) to ensure
sufficient solvent removal. The extraction and recovery procedure took from 3 to 4 hrs for each
specimen. Two replicates were extracted and recovered for each mixture, and the properties of
the recovered binders were compared to each other. When inconsistencies occurred in these
recovered binder properties, additional replicates were extracted, up to four replicates total for a
given mixture (99).
BINDER TESTS
Binder tests conducted included size exclusion chromatography, dynamic shear
rheometry, ductility, and fourier transform infrared spectroscopy. These tests are discussed in the
next sections, and results are presented and discussed in Chapters 9 and 11.
Size Exclusion Chromatography
After extraction and recovery, the binder was analyzed using Size Exclusion
Chromatography (SEC) to ensure complete solvent removal. Test samples were prepared by
dissolving 0.2 ± 0.005 g of binder in 10 mL of tetrahydrofuran (THF). The sample then was
sonicated for 30 minutes to ensure complete dissolution and filtered through a 0.45µm
polytetrafluoroethylene (PTFE) syringe filter. Samples of 100 µL were injected into 1000, 500,
and 50 Å columns in series with THF carrier solvent flowing at 1.0 mL/min.
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The chromatograms of binders obtained from the same replicate should overlay each
other. If there was any solvent residue in the binder, there was a peak located at 38 minutes on
the chromatogram (100).
Dynamic Shear Rheometer
A Carri-Med CSL 500 Controlled Stress DSR Rheometer measured the rheological
properties of the binder.
The rheological properties of interest were the complex viscosity (η) measured at 60 oC
(140 °F) and 0.1 rad/s (approximately equal to the low-shear rate limiting viscosity) and the
storage modulus (G’) and the dynamic viscosity (η’), both at 45 °C (113 °F) and 10 rad/s
measured in a frequency sweep mode. A 2.5 cm (0.98 inches) composite parallel plate geometry
was used with a 500 mm (19.5 inches) gap between the plates.
These rheological properties were used to understand how the physical properties of the
binder changed with time. DSR measurements also were important for deciding whether the
binder was changed in some way by the extraction and recovery process (98-100). If two
extraction and recovery processes yielded binders with matching SEC chromatograms but
significantly different complex viscosities, then at least one of the binders was suspected of
having undergone solvent hardening or softening.
Ductility
Ductilities for long-term aged original binder, aged 3 and 6 months in a 60 oC (140 °F)
room after SAFT for this report, were measured at 15 oC (59 °F) and an extensional speed of 1
cm (0.39 inches) per minute in accordance with ASTM D 113-86 (101). The ductility sample,
which had been made in a mold, had a 3 cm (1.18 inches) initial gauge length and a tapered
throat. The ductility was taken as the amount of extension in centimeters of the asphalt specimen
when the binder fractured at the tapered throat.
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Fourier Transform Infrared Spectroscopy
Carbonyl area (CA) was measured using a Galaxy 5000 fourier transform infrared
spectroscopy (FTIR) spectrometer with an attenuated total reflectance (ATR) zinc selenide prism
(99). CA is the area under the absorption band from 1650 to 1820 cm-1 (4231 to 4667 inches-1)
and relates directly to the oxygen content in the asphalt binder, and thus increases in CA are used
to quantify oxidative aging (102, 103).
SUMMARY
The bullets below provide a summary of binder oxidative hardening in relation to HMAC
mixture fatigue resistance and the testing methodology utilized in this project to characterize this
phenomenon:
• Binder oxidative aging is a major contributor to age-related pavement failure. The prime
objective of this chapter was to present a background of binder oxidative aging and analysis
methodology as a context for understanding the effect of binder aging on HMAC mixture
fatigue resistance, presented in Chapters 9 and 11.
• Over time, binders experience oxidative age-hardening that increases their elastic stiffness
and simultaneously reduces their ability to flow or relieve stress, thus making the binders
more brittle.
• The DSR function map of G’ versus η’/G’ is a useful method for tracking changes in a
binder’s rheology with aging in a way that relates at least for unmodified binders to binder
ductility and, we hypothesize, to HMAC pavement durability.
• The DSR, ductility, SEC and FTIR were the tests utilized in this project to characterize the
binder rheological and chemical properties of binders.
Page 165
145
CHAPTER 9 BINDER-HMAC MIXTURE CHARACTERIZATION
Pavements deteriorate over time and eventually require maintenance or rehabilitation.
While fatigue is considered to be a major factor leading to failure, binder embrittlement due to
oxidative aging almost certainly plays a significant role as well. One objective of this project
was to better understand the impact of oxidative aging on mixture fatigue resistance and on other
mixture properties in general.
Mixture fatigue studies and the extent to which it is impacted by oxidative aging are
documented elsewhere in this report. The effect of binder oxidative aging on fatigue was found
to be significant.
The purpose of the work reported in this chapter was to address other binder-mixture
relations besides fatigue. Of particular interest was the impact of binder aging on mixture
stiffness, as characterized by the mixture’s visco-elastic properties, and the relation of these
mixture properties to changes in binder properties.
Loose mix, aged according to AASHTO PP2 4 hrs short-term aging, was compacted,
tested in a nondestructive relaxation modulus procedure, aged further in a 60 °C (140 °F)
environmental room for intervals of 3 months (from 0 to 6 months), and tested again after each
of these aging intervals. In this way, the same physical specimen was tested at each aging level
so that the effect of binder aging could be determined independent of other mixture variables.
Replicate compacted mixture specimens were aged for the specified intervals and the binder
recovered and tested for DSR properties that could be compared to the mixture properties.
The remainder of this chapter provides further details of binder and mixture experimental
procedures, analysis procedures, and test results.
Page 166
146
AASHTO PP2 (135 °C for 4 hrs, Compact)
Extract & Recover Binders
Age @ 60 oC for 3, 6 Months
Binder Tests
Binder in Mixtures
METHODOLOGY
Changes in binder properties with aging are to be associated with changes in mixture
properties, with the objective of learning how to predict changes in mixture fatigue lives due to
binder stiffening by aging. Two different binders were used: a PG 64-22 from a basic mixture
design (denoted as the Bryan mixture) and a PG 76-22 from a rutting resistance mixture design
(denoted as the Yoakum mixture). Binders in mixtures were conditioned and tested as shown in
Figure 9-1.
Figure 9-1. Binder Oxidative Aging and Testing
(°F = 32 + 1.8(°C)).
Binder aging and the extraction and recovery process were explained in Chapter 8. The binder
tests included size exclusions chromatography and dynamic shear rheometry; details are also
described in chapter 8.
Page 167
147
Binder Data Analysis
'G and "G values were measured at three different temperatures (20, 40, 60 oC) (68, 104,
140 °F), and master-curves for 'G , "G were constructed using time-temperature superposition
(TTSP) at 20 oC (68 °F). Shift factor data as a function of temperature were modeled as shown in
Equation 9-1 (104):
1
2
( )log
( )ref
Tref
C T Ta
C T T− −
=+ −
(Equation 9-1)
where:
Ta = The shift factor at temperature T relative to the reference temperature refT
1 2,C C = Empirically determined coefficients
T = The selected temperature of interest, oC or K
refT = The reference temperature, oC or K
In addition to master-curves, the DSR function ( '/( '/ ')G Gη ), measured at 44.7 oC
(112.5 °F), 10 rad/sec but shifted to 15 oC (59 °F) 0.005 rad/sec by (TTSP), was used to track
changes in binders with oxidative aging (96).
HMAC Mixture Tests
The binder-mixture (BM) test protocol was similar to the CMSE relaxation modulus test
described in Chapter 6, except that the same HMAC specimen was repeatedly tested at different
aging conditions. Thus, data were obtained at each test temperature for which the only variable
mixture parameter was the aging condition of the binder; other mixture parameters (Void in
Mineral Aggregates (VMA), Void Filled with Asphalt (VFA), aggregate size distribution, and
configuration, etc.) were identical within the same specimen. The test was performed with both
mixtures (Bryan and Yoakum) at 0, 3 and 6 months aging conditions with at least two replicate
specimens for each mixture.
Page 168
148
Figure 9-2 is a schematic illustration of the BM characterization test plan with RM
testing.
Figure 9-2. Binder-Mixture Characterization Test Procedure (°F = 32 + 1.8(°C)).
Chapter 5 describes the RM test conditions and loading configuration. Note that RM
testing in this project was assumed non-destructive.
AASHTO PP2(HMAC Mixture @ 135 °C for 4 hrs, compact)
3rd RM Testing @ 10, 20, & 30 oC
(Total aging period = PP2 + 0 months)
Age HMAC compacted specimens @ 60 oC for 3 months (Total aging period = PP2 + 3 months)
Age HMAC compacted specimens @ 60 (Total aging period = PP2 + 6 months)
oC for 3 more months
1st RM Testing @ 10, 20, & 30 oC
2nd RM Testing @ 10, 20, & 30 oC
Page 169
149
HMAC Mixture Visco-Elastic Characterization
The data obtained from the tensile RM test includes the time-dependent elastic relaxation
modulus (E(t)), loading time (t), and test temperature (T). From these data, mixture visco-elastic
properties were determined for comparison with the binder visco-elastic properties. The
following procedure was used to estimate the mixture visco-elastic properties.
Elastic Modulus (E(t)) Master-Curve
A master-curve for E(t) was constructed at a reference temperature of 20 oC (68 °F) from
the data obtained at three different temperatures (10, 20, and 30 oC) (50, 68, and 86 °F) by using
the Williams-Landel-Ferry (WLF) TTSP procedures (104, 105). As an example, the master-
curve for E(t) in Figure 9-3 was constructed from data for a Yoakum mixture used for the
CMSE procedure.
Figure 9-3. Relaxation Master-Curve for 0 Month Aged
Yoakum Mixture Used for CMSE (°F = 32 + 1.8(°C)).
10-1 100 101 102 103 104101
102
103
104
Yoakum MixtureRef T=20
oC
Cal-E(t), MixPP2+0M from CMSE E(t), MixPP2+0M from CMSE
E(t)
(MPa
)
Reduced Time (sec)
E1=1000; m=0.011ln(tr)+0.46
Page 170
150
1 1 1( )( )
mm m
r r rT
tE t E E t E t Ea T
−
− −∞
⎛ ⎞= + ≅ = ⎜ ⎟
⎝ ⎠
( )rm aLn t b= +
While there are some obvious inconsistencies in the data, E(tr) was found to be well
represented by the model given by Equations 9-2 and 9-3:
(Equation 9-2)
(Equation 9-3)
where:
E(t), E(tr) = Time-dependent elastic modulus at time t (MPa)
E1 = Initial (tr = 1 sec) elastic modulus (MPa)
t = Time (s)
tr = Reduced time (s)
T = Temperature (oC)
a, b = Empirically determined coefficients
aT(T) = The shift factor at temperature T relative to
the reference temperature refT
The elastic modulus obtained by the RM test is a function of time because of the
visco-elastic nature of the HMAC mixture. Under deformation, the stress builds because of the
mixture’s elastic nature but then relaxes at fixed strain because of its ability to undergo viscous
flow. This relaxation is reflected in the decrease of E(tr) over time in the RM test. Therefore,
storage (elastic) and loss (viscous) moduli can be calculated from the E(tr) master-curve.
The m value in Equation 9-2 was assumed to be a function of time and temperature
according to Equation 9-3. Once the temperature shift factors are determined through TTSP
alignment of the data, and the model parameters E1, a, and b are estimated, E(tr) can be
calculated. Figure 9-3 shows the result for this example.
( )rT
tta T
=
Page 171
151
12 rt
ω ≅
1(1 )( )
2m
m mG G cos πωω −
Γ − ⎛ ⎞= ⎜ ⎟⎝ ⎠
'
1(1 )"( )
2m
m mG G sin πωω −
Γ − ⎛ ⎞= ⎜ ⎟⎝ ⎠
( )1
2 2 2*( ) ( ') ( ")G G Gω = +
11
( )( ) , 2(1 ) 2(1 )
rr
E t EG t Gν ν
= =+ +
Dynamic Mixture Storage and Loss Moduli
The elastic modulus is converted to a shear modulus according to Equation 9-4:
(Equation 9-4)
Converting to frequency by Equation 9-5:
(Equation 9-5)
the dynamic shear storage ( 'G ) and loss ( "G ) moduli are calculated by (45, 108):
(Equation 9-6)
and
(Equation 9-7)
and the magnitude of the complex dynamic shear modulus (G*) is given by:
(Equation 9-8)
where:
tr = Reduced time (s)
t = Actual loading time (s)
aT(T) = Temperature shift factor
m = Exponential stress relaxation rate (0 ≤ m < 1)
ν = Poisson’s ratio (≅ 0.33)
Page 172
152
G(t), G(tr) = Time-dependent shear modulus at time t ( MPa)
G1 = Initial shear modulus (MPa)
'( )G ω = Elastic (storage) dynamic shear modulus (MPa)
"( )G ω = Viscous (loss) dynamic shear modulus (MPa)
G*(ω) = Complex dynamic shear modulus (MPa)
Γ = Gamma function
For ν, the research team used a value of 0.33 for the HMAC mixture consistent with the
work done by Huang and Lytton et al. (45, 106). Γ is the Lap lace (or Euler) Gamma
transformation function that is widely used in many mathematical engineering applications.
The results of this procedure for the Yoakum mixture are shown in Figure 9-4. Note that
at higher frequencies (lower temperatures) the storage modulus dominates the loss modulus,
whereas at lower frequencies the reverse is true, typical of visco-elastic materials.
Mixture Visco-elastic (VE) Function
A visco-elastic function for mixtures can be calculated that is analogous to the DSR
function for binders. As a first trial in this project, an angular frequency was arbitrarily selected
where "/ 'G G is of the order of unity at 20 oC (68 °F), as it is for an aged binder at 15 oC (59
°F), 0.005 rad/sec. In this way, it was hoped that aging of the mixture would be readily observed
from the visco-elastic properties. If the frequency is too high or the temperature too low, then the
mixture would reflect elastic limit properties and not be sensitive to aging. So the VE function
was calculated as follows:
VE function = '/( "/( ' ))G G G ω at 20 oC (68 °F), 0.002 rad/sec (Equation 9-9)
Page 173
153
Figure 9-4. Shear Modulus Master-Curve for 0 Month Aged Yoakum Mixture used for
CMSE (°F = 32 + 1.8(°C)).
RESULTS
The test results are presented in three sections: recovered binder properties, mixture
visco-elastic properties, and binder-mixture relationships. As discussed at the beginning of this
chapter, aged mixture samples were prepared using the PP2 4-hr short-term procedure. This
aged mixture was then used to make replicate compacted mixtures. One of these replicates was
tested as is (PP2 + 0 months), then aged for three months in the 60 °C (140 °F) environmental
room (PP2 + 3 months) and tested again. The mixture test was the RM test conducted at 10, 20,
and 30 °C (50, 68, and 86 °F). This same specimen has now been aged to a total of 6 months,
but the testing was not complete in time for this report. Instead, a separate replicate sample was
aged for 6 months (PP2 + 6 months), and the corresponding RM data are reported in this chapter.
Binder was recovered from other replicate compacted and aged mixture samples and tested to
provide binder properties to compare to the tested mixtures. From both binder properties and the
corresponding mixture properties, the effect of binder hardening on mixtures was evaluated
directly and without the variability created by mixture parameters other than binder rheology.
10-4 10-3 10-2 10-1 100 101101
102
103
104
Yoakum Mixture from CMSE
G'(w)-MixPP2+0M G"(w)-MixPP2+0M G*(w)-MixPP2+0M
G',
G",
G* (
MPa
)
Angular Frequency (rad/sec)
Ref T=20 o
C
Page 174
154
Recovered Binder Results
Binder master-curves for the dynamic shear storage '( )G ω , loss "( )G ω , and complex
*( )G ω moduli were used to track changes in binder properties with aging. Figures 9-5 to 9-8
show the results for binders recovered from Bryan and Yoakum mixtures at three levels of aging.
Figures 9-5 and 9-6 show that the complex moduli increase with aging for both
unmodified (Bryan) and modified (Yoakum) binders. Figures 9-7 and 9-8 show that '( )G ω and
"( )G ω increase with aging. Furthermore, '( )G ω is greater than "( )G ω at high frequency, and
"( )G ω is greater than '( )G ω at low frequency at each aging level.
Page 175
155
Figure 9-5. Master-Curves of Recovered Binders for G*(ω) from Bryan Mixture
(°F = 32 + 1.8(°C)).
.
Figure 9-6. Master-Curves of Recovered Binders for G*(ω) from Yoakum Mixture
(°F = 32 + 1.8(°C)).
10-5 10-4 10-3 10-2 10-1 100 101102
103
104
105
106
Ref T=20 o
C
G*(PP2+0M) G*(PP2+3M) G*(PP2+6M)
G*(
Pa)
Angular Frequency (rad/sec)
Recovered Binder from Yoakum Mixture
10-5 10-4 10-3 10-2 10-1 100 101102
103
104
105
106
Ref T=20 o
C
G*(PP2+0M) G*(PP2+3M) G*(PP2+6M)
G*(
Pa)
Angular Frequency (rad/sec)
Recovered Binder from Bryan Mixture
Page 176
156
10-5 10-4 10-3 10-2 10-1 100 101101
102
103
104
105
106
Ref T=20 o
C
G'(PP2+0M) G"(PP2+0M) G'(PP2+3M) G"(PP2+3M) G'(PP2+6M) G"(PP2+6M)
G',
G"
(Pa)
Angular Frequency (rad/sec)
Recovered Binder from Bryan Mixture
10-5 10-4 10-3 10-2 10-1 100 101101
102
103
104
105
106
Ref T=20 o
C
G'(PP2+0M) G"(PP2+0M) G'(PP2+3M) G"(PP2+3M) G'(PP2+6M) G"(PP2+6M)
G',
G"
(Pa)
Angular Frequency (rad/sec)
Recovered Binder from Yoakum Mixture
Figure 9-7. Master-Curves of Recovered Binders for '( )G ω , "( )G ω from Bryan Mixture (°F = 32 + 1.8(°C)).
Figure 9-8. Master-Curves of Recovered Binders for '( )G ω , "( )G ω from Yoakum Mixture (°F = 32 + 1.8(°C)).
Page 177
157
DSR map aging paths for the binder recovered from aged Bryan and Yoakum mixtures
are shown in Figures 9-9 and 9-10, respectively.
In each case, the recovered binder moves upward and to the left with aging, as has been
observed previously with neat binder aging (52, 96). Interestingly, these two binder paths very
nearly overlap each other, although the Yoakum binder is stiffer than the Bryan binder at each
level of aging.
The curved, dashed lines shown are lines of constant ductility (cm at 15 oC, 1 cm/min)
(59 °F, 0.39 inches/min) that were determined for unmodified binders by Ruan et al. (52, 96); as
a binder ages, its ductility decreases. Kandhal (107) concluded that a ductility of 3 cm (1.18
inches) at 15 oC (59 °F) is a value that corresponds well to age-related cracking failure in HMAC
pavements.
Figure 9-9. DSR Function of Recovered Binders from Bryan Mixture (°F = 32 + 1.8(°C)).
100 200 300 400 500 600 700 8000.01
0.1
1
8
10
5
6
3 42
PP2 PP2+3M PP2+6M
G'(M
Pa)(
15 o C
, 0.0
05 ra
d/s)
η'/G'(s)( 15 oC, 0.005 rad/s)
Recovered Bryan DSR map
Page 178
158
100 200 300 400 500 600 700 8000.01
0.1
1
8
10
5
6
3 42
PP2 PP2+3M PP2+6M
G'(M
Pa)(
15 o C
, 0.0
05 ra
d/s)
η'/G'(s)( 15 oC, 0.005 rad/s)
Recovered Yoakum DSR map
Figure 9-10. DSR Function of Recovered Binders from Yoakum Mixture
(°F = 32 + 1.8(°C)).
Page 179
159
10-1 100 101 102 103 104101
102
103
104
Bryan MixtureRef T=20
oC
Cal-E(t), MixPP2+0M E(t), MixPP2+0M Cal-E(t), MixPP2+3M E(t), MixPP2+3M Cal-E(t), MixPP2+6M E(t), MixPP2+6M
E(t)
(MPa
)
Reduced Time (sec)
HMAC Mixture Results
Following the procedure described in the previous section for mixture analysis, tensile
RM master-curves were determined for both the Bryan and Yoakum mixtures. The results at a
reference temperature of 20 °C (68 °F) are presented in Figures 9-11 and 9-12.
Figure 9-11. Master-Curves of Bryan Mixture for E(t) (°F = 32 + 1.8(°C)).
Clearly, there are inconsistencies in the data, most notably toward the end of each
relaxation test, that make the master-curve determination problematic. The value of m in
Equation 9-2 is assumed to be a function of time (through Equation 9-3) to allow the master-
curves to be non-linear on the log-log plot, but the amount of curvature built into the model by
the value of a in Equation 9-3 is somewhat subjective. In addition, it is necessary to place
unequal weighting on different parts of each relaxation experiment when performing the time-
temperature shifting, and this weighting also is somewhat subjective. The net effect is that the
master-curves necessarily are subject to some degree of uncertainty. Additional experience with
this method and independent verification with other experiments (dynamic modulus, for
example) is necessary in order to achieve more confidence in the mixture visco-elastic
properties.
Page 180
160
Figure 9-12. Master-Curves of Yoakum Mixture for E(t) (°F = 32 + 1.8(°C)).
.
Note that the data for the PP2 and PP2 plus 3 months aging levels were obtained on the
same mixture specimens for both the Bryan and Yoakum mixtures. The PP2 plus 6 months data
for each mixture were from a different specimen, one used for the CMSE data analysis. Six-
month data on the 0 and 3 month specimens will be obtained as part of this project to complete
the 0, 3, and 6 month series on a single specimen.
The objective of obtaining a set of data at different aging levels from the same mixture
specimen is to study the effect of binder aging alone on mixture stiffness and visco-elastic
behavior. If different specimens are studied, then the whole host of mixture variables (aggregate
gradation, VMA, VFA, binder content, and aggregate alignment configuration) is brought in to
play, and greater variability in the aging data would result.
Clearly, oxidative aging stiffens the tensile RM of the mixture significantly, consistent
with stiffening of the neat binder with aging. Also noted is that the Bryan mixture is stiffer than
the Yoakum mixture at comparable levels of aging and test condition.
10-1 100 101 102 103 104101
102
103
104
Yoakum Mixture
Ref T=20 o
C
Cal-E(t), MixPP2+0M E(t), MixPP2+0M Cal-E(t), MixPP2+3M E(t), MixPP2+3M Cal-E(t), MixPP2+6M E(t), MixPP2+6M
E(t)
(MPa
)
Reduced Time (sec)
Page 181
161
From these tensile RM master-curves, dynamic shear moduli master-curves, also at a
reference temperature of 20 °C (68 °F), were calculated as defined by Equations 9-4 through 9-8.
The results are given in Figure 9-13 ( 'G , "G ) for the Bryan mixtures and in Figure 9-14
( 'G , "G ) for the Yoakum mixtures.
Figure 9-13. Master-Curves of Bryan Mixture for '( )G ω , "( )G ω (°F = 32 + 1.8(°C)).
Again, stiffening of the mixture with oxidative aging is evident as 'G , "G , and *G all
increase, and the crossover frequency (frequency at which ' "G G= ) moves to a lower frequency.
The effects of 60 °C (140 °F) aging for 0, 3, and 6 months beyond PP2 conditioning are evident
in Figures 9-11 and 9-12.
In addition, Figure 9-15 compares the complex dynamic shear moduli ( *G ) of the Bryan
and Yoakum mixtures. Note that *G increases with aging for both mixtures, and the Bryan
mixture is stiffer than the Yoakum mixture, which is most evident at the lower frequencies.
10-4 10-3 10-2 10-1 100 101101
102
103
104
Bryan Mixture
G'(w)-MixPP2+0M G"(w)-MixPP2+0M G'(w)-MixPP2+3M G"(w)-MixPP2+3M G'(w)-MixPP2+6M G"(w)-MixPP2+6M
G',G
"(M
Pa)
Angular Frequency (rad/sec)
Ref T=20 o
C
Page 182
162
Figure 9-14. Master-Curves of Yoakum Mixture for '( )G ω , "( )G ω (°F = 32 + 1.8(°C)).
Figure 9-15. Master-Curve Comparisons between Bryan and Yoakum Mixtures for G*(ω)
(°F = 32 + 1.8(°C)).
10-4 10-3 10-2 10-1 100 101101
102
103
104
Yoakum Mixture
G'(w)-MixPP2+0M G"(w)-MixPP2+0M G'(w)-MixPP2+3M G"(w)-MixPP2+3M G'(w)-MixPP2+6M G"(w)-MixPP2+6M
G',G
"(M
Pa)
Angular Frequency (rad/sec)
Ref T=20 o
C
10-4 10-3 10-2 10-1 100101
102
103
Bryan vs Yoakum Mixtures
Ref T=20 o
C
BRY-MixPP2+0M BRY-MixPP2+3M BRY-MixPP2+6M YKM-MixPP2+0M YKM-MixPP2+3M YKM-MixPP2+6M
G*(
MPa
)
Angular Frequency (rad/sec)
Page 183
163
Similar to the DSR map for the recovered binders, a visco-elastic property aging map can
be constructed from the mixture visco-elastic master-curves. As described previously, values
from the 20 °C (68 °F) reference master-curves at 0.002 rad/s were used to plot 'G versus
'/ 'Gη , and the results are shown in Figures 9-16 (Bryan) and 9-17 (Yoakum). Remember that
the PP2+6 months data are from different HMAC mixture specimens than the PP2+0 and PP2+3
months data.
Figure 9-16. VE Function of Bryan Mixture (°F = 32 + 1.8(°C)).
100 200 300 400 500 600 700 80010
100
1000
Mix PP2+0M Mix PP2+3M Mix PP2+6M
G'(M
Pa)(
20 o C
, 0.0
02 ra
d/s)
η'/G'(s)( 20 oC, 0.002 rad/s)
VE map for Bryan Mixture
Page 184
164
100 200 300 400 500 600 700 80010
100
1000
Mix PP2+0M Mix PP2+3M Mix PP2+6M
G'(M
Pa)(
20 o C
, 0.0
02 ra
d/s)
η'/G'(s)( 20 oC, 0.002 rad/s)
VE map for Yoakum Mixture
Figure 9-17. VE Function of Yoakum Mixture (°F = 32 + 1.8(°C)).
Binder-Mixture Comparisons
The mixture trends are obvious and very similar to the recovered binder DSR map. With
aging, the mixture moves to the left and upward due to binder stiffening. The good correlation
between the mixture and binder maps is shown in Figure 9-18, where the VE function
( '/( '/ ')G Gη ) is plotted against the DSR function. Interestingly, the slopes of the Bryan and
Yoakum plots are virtually identical, and differences are manifested primarily in an offset
(magnitude) of the two sets of data.
Page 185
165
Figure 9-18. VE Function vs. DSR Function (°F = 32 + 1.8(°C)).
SUMMARY
In this project, two HMAC mixtures were tested to obtain mixture visco-elastic properties
at three conditions (0, 3, and 6 months) of binder aging. Nondestructive tensile RM tests were
used to produce mixture dynamic shear storage and loss moduli master-curves. Binders
recovered from aged mixtures were used to determine corresponding master-curves for the
binder. From these binder-mixture aging experiments, the following results were obtained:
• Mixtures stiffen significantly in response to binder oxidative aging. Mixture stiffening
was reflected in both the tensile relaxation modulus and the dynamic shear moduli.
10-4 10-3 10-210-2
10-1
100
101
Yoakum Bryan
Mix
ture
(G
'/(η
'/G')
, MPa
/s),
20
o C, 0
.002
rad/
s
Binder ( G'/( η'/G') , MPa/s) , 15 oC, 0.005 rad/s
Page 186
166
• A mixture visco-elastic property map of 'G versus '/ 'Gη at the three levels of mixture
aging (PP2, PP2+3 months, PP2+6 months) provided a useful means of tracking mixture
stiffening with binder oxidative aging. This mixture VE map is analogous to the binder
DSR map developed in Project 0-1872 (52).
• A mixture VE function, defined as '/( '/ ')G Gη at 20 °C (68 °F), 0.002 rad/s correlated
linearly with the binder DSR function '/( '/ ')G Gη at 15 °C (59 °F), 0.005 rad/s.
• The Bryan (PG64-22) binder is softer than the Yoakum (PG76-22) binder. However, the
Bryan mixture is stiffer than the Yoakum mixture, at comparable angular frequency or at
comparable binder stiffness.
Page 187
167
CHAPTER 10 HMAC MIXTURE RESULTS AND ANALYSIS
This chapter presents the mixture results analyzed at a typical 95 percent reliability level.
For simplicity and because HMAC fatigue cracking is generally more prevalent at intermediate
pavement service temperatures, most of the laboratory tests were conducted at 20 °C (68 °F).
Otherwise, the results were normalized to 20 °C (68 °F).
MIXTURE PROPERTIES FOR PREDICTING Nf
Laboratory test results for mixture properties related to Nf predictions are presented in
this section for the three aging conditions (0, 3, and 6 months) for both Bryan and Yoakum
mixtures. These results, which include BB, tensile strength, relaxation modulus, DPSE, SE,
anisotropy, and dynamic modulus, represent mean values of at least two test specimens.
BB Laboratory Test Results
Table 10-1 is a summary of the BB fatigue test results conducted at two test strain levels
(374 and 468 microstrain) at 20 °C (68 °F) and 10 Hz frequency. These results are an average of
at least two test specimens per mixture type per aging condition. Detailed results are attached in
Appendix C.
Table 10-1. BB Laboratory Test Results.
Mean N Value Aging Condition
Bryan @ 374 Test
Microstrain
Bryan @ 468 Test
Microstrain
Yoakum @ 374 Test
Microstrain
Yoakum @ 468 Test
Microstrain
0 months 127,000 50,667 223,790 105,350
3 months 80,187 39,833 172,167 86,187
6 months 53,000 27,500 108,200 47,150
Page 188
168
In Table 10-1, N (without subscript f) refers to the average number of laboratory load
cycles or repetitions to fatigue failure during the BB test. Fatigue failure, as defined in Chapter 4,
is the point of 50 percent reduction in the initial HMAC flexural stiffness measured at the 50th
load cycle (2, 59). From Table 10-1, while N decreased significantly with aging for both
mixtures, the Yoakum mixture sustained higher N values at both strain levels for all aging
conditions compared to the Bryan mixture.
The reduction in N, which was approximately 25 and 50 percent after 3 and 6 months
aging, respectively, indicates that aging has a very significant effect on the HMAC mixture
fatigue resistance. The relatively higher N for the Yoakum mixture was possibly due to the
higher binder content (5.6 percent compared to 4.6 percent for the Bryan mixture by weight of
aggregate) and the effect of the SBS modifier.
Nf-εt Empirical Relationships
Figures 10-1 (a) and (b) show plots of the average N versus test εt on a log-log scale.
Based on these figures, empirical fatigue relationships of the power format shown in Table 10-2
were derived and used to estimate lab Nf. These empirical fatigue equations and material
constants (ki) in Table 10-2 were derived by fitting power regression trend lines through the N
data points in Figure s 10-1 (a) and (b), and were also checked using least squares line regression
analysis. Each N data point in Figure 10-1 is a mean value of three replicate measurements.
Table 10-2. Mixture Empirical Fatigue Relationships.
Materials Constants Aging Condition
Mixture Equation k1 k2
Bryan ( ) 0984.49101 −−×= tfN ε 1 × 10-9 4.0984 0 months
Yoakum ( ) 3603.37107 −−×= tfN ε 7 × 10-7 3.3603
Bryan ( ) 1205.36102 −−×= tfN ε 2 × 10-6 3.1205 3 months
Yoakum ( ) 0861.36105 −−×= tfN ε 5 × 10-6 3.0861
Bryan ( ) 9263.26105 −−×= tfN ε 5 × 10-6 2.9263 6 months
Yoakum ( ) 7047.38102 −−×= tfN ε 2 × 10-8 3.7047
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1.0E+04
1.0E+05
1.0E+06
1.0E+07
100 1000
Microstrain
Load
Cyc
les
(N)
Bryan, 0 MonthsBryan, 3 MonthsBryan, 6 Months
Figure 10-1(a). N vs. εt at 20 °C (68 °F) (Bryan Mixture).
1.0E+04
1.0E+05
1.0E+06
1.0E+07
100 1000
Microstrain
Load
Cyc
les
(N)
Yoakum, 0 MonthsYoakum, 3 MonthsYoakum, 6 Months
Figure 10-1(b). N vs. εt at 20 °C (68 °F) (Yoakum Mixture).
Note that the fatigue results in Figure 10-1 were based on two test strain levels for each
mixture per aging condition. For better Nf predictions and statistical analysis, more data points
(collected at more than two test strain levels) are recommended. Generally, more testing at
different strain levels would lead to a better fatigue relationship, but bearing in mind that BB
testing is quite a lengthy test. However, each data point in Figure 10-1 is a mean value of three
replicate measurements of different HMAC beam specimens.
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Tensile Strength (σt)
Table 10-3 is a summary of the average σt results measured at 20 °C (68 °F).
Figures 10-2(a) through 10-2(c) are examples of plots of tensile stress and strain at break as a
function of aging condition for each mixture.
Table 10-3. Mixture Tensile Strength.
Aging Condition Mixture Mean σt @
Break (psi)
Mean Tensile Strain (εf)
@ Break
Bryan 105 1245 × 10-6 0 months
Yoakum 123 3483 × 10-6
Bryan 112 689 × 10-6
3 months Yoakum 152 2342 × 10-6
Bryan 157 401 × 10-6
6 months Yoakum 184 851 × 10-6
Table 10-3 indicates that as the HMAC ages, it becomes more brittle, thus breaking under
tensile loading at a lower strain level (Figure 10-2). For both mixtures, the failure strain (εf) at
break decreased significantly on the order of at least 30 percent per mixture type. The research
team attributed this phenomenon to an increase in mixture brittleness due to binder oxidative
aging.
In terms of mixture comparison, the σt and εf values for the Yoakum mixture were higher
than that of the Bryan mixture at all aging conditions, indicating that for the test conditions
considered in this project:
• the Yoakum mixture was more ductile than the Bryan mixture, and
• the Yoakum mixture had a better resistance to tensile stress than the Bryan mixture.
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0
50
100
150
200
0 500 1000 1500 2000 2500 3000 3500 4000
Microstrain
Tens
ile S
tress
(psi
)
Bryan, 0 MonthsBryan, 3 MonthsBryan, 6 Months
Figure 10-2(a). Mixture Tensile Stress at 20 °C (68 °F) (Bryan Mixture).
0
50
100
150
200
0 500 1000 1500 2000 2500 3000 3500 4000
Microstrain
Tens
ile S
tress
( ps
i)
Yoakum, 0 Months
Yoakum, 3 Months
Yoakum, 6 Months
Figure 10-2(b). Mixture Tensile Stress at 20 °C (68 °F) (Yoakum Mixture).
Figure 10-2(c) is a plot of the εf values as a function of aging condition. The figure shows
the expected decreasing trend of the εf values at 20 °C (68 °F) as a function of binder oxidative
aging due to increasing mixture brittleness. The increased ductility of the Yoakum mixture is
apparent and is indicated by the comparatively higher εf values at all aging conditions, which are
almost double the Bryan mixture εf values.
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172
100
1,000
10,000
0 3 6
Aging Period (months)
Failu
re M
icro
stra
in
Bryan
Yoakum
Figure 10-2(c). Mixture Failure Tensile Strain (εf) at Break at 20 °C (68 °F).
Relaxation Modulus Master-Curves The RM test results in terms of the E1 and m values are summarized in Table 10-4, and
some examples are presented graphically in Figure 10-3 on a log-log scale. As expected, E1
increased with aging due to HMAC hardening and stiffening effects from oxidation of the
binder. This stiffening effect, however, also causes the material property parameter m, which
describes the rate at which the mixture relaxes the applied stress, to decrease. For visco-elastic
materials like HMAC, the higher the m value, the higher the ability of the mixture to relax the
stress and the greater the resistance to fracture damage.
Table 10-4. Mixture Relaxation Modulus (Tension) Test Data.
Average E1 (psi) Average m Aging Condition Bryan Yoakum Bryan Yoakum
0 months 208,100 178,785 0.3997 0.5116
3 months 675,600 389,325 0.3774 0.4513
6 months 1,010,215 633,505 0.2945 0.4273
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Note that the E(t) values in Figures 10-3(a) and (b) are plotted in metric units (where 1 MPa
≅ 145 psi). This was done in order to allow for easy comparison with the binder-HMAC mixture
master-curves discussed in Chapter 9 (which includes binder test results). Note that metric units
are typically used for binder test results, which is consistent with the PG specification used by
TxDOT for binders.
RM (Tension) Master-Curves, Tref = 20 oC
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
0.01 0.1 1 10 100 1000 10000
Reduced Time (s)
E(t)
(MP
a)
Bryan, 0 MonthsBryan, 3 MonthsBryan, 6 Months
Figure 10-3(a). RM (Tension) Master-Curve at 20 °C (68 °F) (Bryan Mixture).
RM (Tension) Master-Curves, Tref = 20 oC
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
0.01 0.1 1 10 100 1000 10000
Reduced Time (s)
E(t)
(MPa
)
Yoakum, 0 MonthsYoakum, 3 MonthsYoakum, 6 Months
Figure 10-3(b). RM (Tension) Master-Curve at 20 °C (68 °F) (Yoakum Mixture).
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From Table 10-4 and Figure 10-3, it is clear that the Bryan mixture, although designed
with a softer PG 64-22 binder, was relatively stiffer than the Yoakum mixture. This difference in
the stiffness is particularly more pronounced with aging, indicating that the Bryan mixture was
probably more susceptible to stiffness age-hardening compared to the Yoakum mixture. While
the Yoakum mixture exhibited comparatively lower E1 values, it exhibited higher m values at all
aging conditions. This result indicates that the Yoakum mixture had a relatively better potential
to relax the stress than the Bryan mixture.
Note also that for all aging conditions, the E1 values in compression were higher than the
values in tension and vice versa for the m values. This is an expected material response behavior
due to the generally higher compactive effort in the vertical direction and confirms the
anisotropic nature of HMAC.
RM Temperature Shift Factors, aT
The aT values plotted in Figure 10-4 were computed when generating the RM
master-curves at a reference temperature of 20 °C (68 °F) using the Arrehnius time-temperature
superposition model via spreadsheet SSE regression optimization analysis (84). The almost
overlapping graphs in Figure 10-4 indicate that the aT values are not very sensitive to HMAC
aging. These values, however, exhibit a linear relationship with temperature. Several
researchers, including Christensien et al. (109) have reported similar findings.
When comparing Figures 10-4(a) and 10-4(b), the aT values seem to be material
(mixture) dependent, as evidenced in Equations 10-1 and 10-2:
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175
Log aT = -0.1095T + 2.1978
-2
-1
0
1
2
0 5 10 15 20 25 30 35
Temperature, oC
Log
a T
Bryan, 0 MonthsBryan, 3 MonthsBryan, 6 Months
Figure 10-4(a). Temperature Shift Factors, aT at TRef =20 °C (Bryan Mixture)
(°F = 32 + 1.8(°C)).
Log aT = -0.132T + 2.6711
-2
-1
0
1
2
0 5 10 15 20 25 30 35
Temperature, oC
Log
a T
Yoakum, 0 MonthsYoakum, 3 MonthsYoakum, 6 Months
Figure 10-4(b). Temperature Shift Factors, aT at TRef =20 °C (Yoakum Mixture)
(°F = 32 + 1.8(°C)).
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176
• Bryan mixture
( ) 998.0 ,1978.21095.0 2 =+−= RTaLog T (Equation 10-1)
• Yoakum mixture
( ) 996.0 ,6711.2132.0 2 =+−= RTaLog T (Equation 10-2)
where:
aT = Temperature shift factor
T = Temperature of interest (°C)
Dissipated Pseudo Strain Energy and Fracture Damage
Figure 10-5 is a plot of the rate (denoted as constant b) of HMAC mixture fracture
damage accumulation as a function of the aging condition for each mixture. This constant b was
calculated as the slope of the plot of DPSE versus log N during RDT testing for each mixture
type and aging condition, with the test data normalized to 20 °C (68 °F). This parameter b is an
indicator of the rate of fracture damage accumulation under RDT testing.
0
1
2
3
4
0 3 6
Aging Period (months)
b
BryanYoakum
Figure 10-5. Mixture DPSE at 20 °C (68 °F): Constant b vs. Aging Condition.
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The increasing trend of the b value in Figure 10-5 for both mixtures is indicative that the
rate of fracture damage accumulation increased with aging. The relatively higher b values and
greater rate of change (slope of the graphs in Figure 10-5) of the b value with aging indicates that
the Bryan mixture was accumulating fracture damage at a much faster rate. This observation is
evidence that the Bryan mixture was perhaps more susceptible to fracture damage under RDT
testing than the Yoakum mixture.
Surface Energy
The average measured SE results in terms of ∆Gf and ∆Gh at 20 °C (68 °F) are shown in
Figure 10-6 as a function of aging condition. These SE results shown in Figure 10-6 represent
the mixture adhesive bond strengths under dry conditions in the absence of water at an ambient
temperature of about 20 °C (68 °F). A minimum of two samples were tested per aging
condition.
03
6
Bryan
Yoakum0
50
100
150
200
250
SE (ergs/cm2)
Aging Period (Months)
Figure 10-6(a). Mixture Fracture Energy (∆Gf), ergs/cm2
(adhesive, dry conditions).
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178
03
6
Bryan
Yoakum0
50
100
150
200
250
SE (ergs/cm2)
Aging Period (Months)
Figure 10-6(b). Mixture Healing Energy (∆Gh), ergs/cm2
(adhesive, dry conditions).
Based on simple energy theory concepts, the higher the ∆Gf value, the greater the
resistance to fracture damage, and the lower the ∆Gh value, the greater the potential to self heal.
With these relationships, the Yoakum mixture has a better adhesive bond strength to resist
fracture damage and a stronger potential to self heal, as indicated by the relatively higher fracture
and lower healing energies, respectively, compared to the Bryan mixture.
From the SE results in Figure 10-6, the effect on SFh and Paris’ Law fracture coefficient
A were determined as shown in Table 10-5. Table 10-5 shows that aging has a significant effect
on these parameters (A increased while SFh decreased with aging). Generally, a lower value of A
and higher value of SFh are indicative of greater resistance to fracture and ability to heal,
respectively.
Table 10-5. Paris’ Law Fracture Coefficient A and SFh Value.
Aging Condition Parameter Mixture
0 Months 3 Months 6 Months
Bryan 6.27 × 10-8 16.00 × 10-8 23.43 × 10-8
A Yoakum 5.31 × 10-8 14.01 × 10-8 20.64 × 10-8
Bryan 6.73 4.74 3.07SFh
Yoakum 7.26 4.76 3.81
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For the test conditions considered in this project, these limited SE results indicate that:
• ∆ Gf decreases and ∆Gh increases with aging.
• Binder oxidative aging reduces HMAC mixture resistance to fracture and ability to self
heal. Lytton et al. (94) reported similar findings.
• As indicated by the relatively higher ∆Gf and lower ∆Gh values, respectively, the
Yoakum mixture had a relatively better resistance to fracture damage and potential to self
heal than the Bryan mixture.
In terms of the Yoakum mixture exhibiting relatively better fracture and healing potential
properties, the PG 76-22 plus gravel aggregate for the Yoakum mixture as indicated by the SE
results exhibits a better adhesive bond strength with the corresponding binder than the
component material combination for the Bryan mixture. In other words, the PG 76-22 binder and
gravel aggregates were perhaps more compatible in terms of adhesive bond strength than the PG
64-22 and limestone aggregates for the Bryan mixture. Note that SE data are also often used as a
measure of material compatibility for HMAC mixture characterization.
The high SBS modified binder content could also have possibly played a role in the
relatively better fracture and healing properties of the Yoakum mixture compared to the Bryan
mixture. The research team recommends further laboratory HMAC mixture characterization to
further explore this issue.
Mixture Anisotropy
Table 10-6 shows the SFa results based on mixture AN testing at 20 °C (68 °F). Note that
anisotropy arises due to the fact the HMAC mixture properties, such as the elastic modulus, are
directionally dependent.
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180
Table 10-6. Mixture Anisotropic Results.
SFa Aging Condition
Bryan Yoakum
0 months 1.63 2.10
3 months 1.65 2.08
6 months 2.09 2.40
Average 1.79 2.19
Table 10-8 shows some degree of differences in the SFa results as a function of mixture
type and aging condition. Since anisotropy is predominantly controlled by particle orientation
due to compaction, the theoretical assumption is that HMAC mixtures should exhibit similar
anisotropic response under all aging conditions. Therefore, the cause of discrepancy could be
related to test variability.
Assuming that the SFa differences are primarily due to test variability and mixture
inhomogeneity, the mean SFa values for the Bryan and Yoakum mixtures can be averaged to be
1.79 and 2.19, respectively, for all aging conditions within an error tolerance of 15 percent (110).
In terms of the effect of mixture type, some difference in the SFa values is expected due to the
differences in the aggregate gradation that has an effect on the particle orientation during
compaction. However, since the 1.79 and 2.19 values do not differ by more than 15 percent, a
mean SFa value of 2.0 is not unreasonable for both the Bryan and Yoakum mixtures for all aging
conditions. Aparicio and Oj have reported similar findings (111, 112).
Dynamic Modulus Results
Appendix D includes the mixture |E*| results at 0 months aging condition required for
Level 1 fatigue analysis in the M-E Pavement Design Guide for estimating field Nf. And
Appendix E is an example of the predicted percent fatigue cracking (in terms of area coverage in
the wheelpath) from the M-E Pavement Design Guide software using the HMAC mixture data
contained in Appendix D. Note that because the M-E Pavement Design Guide software
incorporates Global Aging Model analysis in overall field Nf prediction, the research team
considered DM testing of aged mixtures (HMAC specimens) as unnecessary.
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HMAC MIXTURE FATIGUE LIVES (Nf)
In this analysis, the research team defined laboratory fatigue life (lab Nf) as the estimated
HMAC mixture fatigue resistance without inclusion of any shift factors to simulate field
conditions and environmental exposure. Field fatigue life (field Nf ) was then calculated as a
function of the field shift factors and the HMAC laboratory fatigue life (lab Nf).
Throughout this section and subsequent chapters, the units of fatigue life (lab or field Nf)
are defined and expressed in terms of the number of allowable load repetitions to fatigue failure
in the laboratory or traffic ESALs in the field. The reference temperature for all the Nf (lab and
field) results in this section was 20 °C (68 °F).
ME Lab Nf Results
The predicted mixture lab Nf results from ME analysis described in Chapter 4 for the five
pavement structures are attached as Appendix F. These results represent mean values of at least
two test specimens. The overall COV of Ln Nf considering both mixtures (Bryan and Yoakum)
and environmental conditions (WW and DC) ranged between 3.3 percent and 6.8 percent, with a
mean Lab Nf value of about 4.60 × 106. Although the COV seems to be relatively lower when
expressed in terms of Ln Nf, the 95 percent Nf prediction CI margin is very wide, suggesting a
high variability and low precision in the predicted Nf results particularly for the Yoakum mixture
with the modified binder. For example, for PS#1 and WW environment, the mean lab Nf and 95
percent Nf CI are 4.48 × 106 and 2.12 × 106 to 9.46 × 106 for Bryan mixture and 4.11 × 106 and
0.27 × 106 to 62.99 × 106, respectively. Clearly, there is very high variability associated with the
Yoakum mixture for this ME prediction. Inevitably, this result may suggest that the ME
approach utilized in this project may not work well with modified binders, and the results need to
analyzed and interpreted cautiously.
In terms of mixture lab Nf comparison and the effects of aging, Figure 10-7 shows an
example for one pavement structure designated as PS# 1 (Table 3-10) under WW environmental
conditions.
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1.0E+05
1.0E+06
1.0E+07
0 3 6
Aging Period (Months)
Lab
Nf
Bryan Yoakum
Figure 10-7. Mixture Lab Nf at 20 °C (68 °F) for PS#1, WW Environment
(Bryan vs. Yoakum Mixture) – ME Analysis.
For both mixtures, Figure 10-7 shows that Nf decreases with aging, and the Yoakum
mixture generally exhibited relatively higher Nf values compared to the Bryan mixture. This
trend was observed for all pavement structures in both the WW and DC environmental
conditions and is consistent with the prediction from the material property results reported in the
preceding sections.
Ln Nf variability in terms of COV was comparatively higher for the Yoakum mixture, on
the order of about 10 percent more than that of the Bryan mixture. This result is in agreement
with Rowe et al.’s suggestion that while the current ME test protocol and analysis procedure may
work well for unmodified binders (Bryan mixture), it may not be so with modified binders, and
thus the results must be analyzed and interpreted cautiously (113).
CMSE Lab Nf Results
Appendix G contains a list of the mixture Nf results consistent with the CMSE analysis
procedure described in Chapter 5. Like the ME approach, these results represent mean values of
at least two test specimens. In terms of variability, the overall COV of Ln Nf ranged between 1.9
and 2.9 percent.
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The overall 95 percent lab Nf prediction CI was 0.80 × 106 to 13.12 × 106 with a mean lab
Nf value of 6.10 × 106. Considering HMAC mixture inhomogeneity, test variability, and
experimental errors, these results are reasonable and indicate better precision compared to the
ME approach.
For the given pavement structure (PS# 1, Table 3-7) and environmental conditions
(WW), Figure 10-8 indicates that mixture lab Nf decreases with aging and the Yoakum mixture
exhibited higher lab Nf values at all aging conditions. Like the ME approach, this trend was
observed for all pavement structures in both the WW and DC environmental conditions and was
consistent with the measured CMSE mixture material properties.
1.0E+05
1.0E+06
1.0E+07
0 3 6
Aging Period (Months)
Lab
Nf
Bryan Yoakum
Figure 10-8. Mixture Lab Nf at 20 °C (68 °F) for PS#1, WW Environment
(Bryan vs. Yoakum Mixture) – CMSE Analysis.
CM Lab Nf Results
The predicted mixture CM Lab Nf results are tabulated in Appendix J and do not differ
significantly from the CMSE results both in terms of the Nf magnitude and variability.
Essentially, the mixture Nf results and performance trend were similar to the CMSE results for all
pavement structures and environmental conditions for all aging conditions. The mixture Nf,
when plotted as a function of aging condition, is shown in Figure 10-9 for PS# 1 under WW
environmental conditions.
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184
1.0E+05
1.0E+06
1.0E+07
0 3 6
Aging Period (Months)
Lab
Nf
Bryan Yoakum
Figure 10-9. Mixture Nf at 20 °C (68 °F) for PS#1, WW Environment
(Bryan vs. Yoakum Mixture) – CM Analysis.
Figure 10-9 shows that while the mixture Nf generally decreased with aging, the Yoakum
mixture exhibited relatively higher Nf values at all aging conditions. Table 10-7 shows that these
CM results are insignificantly different from the CMSE results. Both of these CM and CMSE
results (Table 10-7) are for the same pavement structure (PS# 1) under WW environmental
conditions.
Table 10-7. CM vs. CMSE Mixture Lab Nf Results for PS#1, WW Environment.
Mixture Lab Nf Aging Condition Mixture
CMSE CM
Difference
Bryan 6.31 × 106 6.29 × 106 -0.32% 0 months
Yoakum 7.88 × 106 7.28 × 106 -7.61%
Bryan 2.42 × 106 2.31 × 106 -4.55% 3 months
Yoakum 4.95 × 106 5.17 × 106 +4.44%
Bryan 0.94 × 106 0.91 × 106 -3.19% 6 months
Yoakum 3.23 × 106 3.13 × 106 -3.10%
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Overall, this correlation between the CM and CMSE Nf results suggests that the CM
approach can be utilized for mixture fatigue analysis in lieu of the CMSE approach, thus
minimizing costs in terms of both laboratory testing and data analysis. Note that SE
measurements (binder and aggregate) and RM tests in compression are not required in the CM
approach. However, this correlation between the CM and CMSE results was expected because
the CM empirical analysis models were modified and calibrated to the CMSE approach as
discussed in Chapter 5. Consequently, more independent HMAC mixtures need to be
characterized for fatigue resistance to validate this CM-CMSE correlation.
Mixture Field Nf Results – ME, CMSE, and CM Analyses
Figure 10-10 is an example of a plot of the field Nf results as a function of aging
condition for PS#1 under WW environmental conditions based on the ME, CMSE, and CM
analyses. Detailed field Nf results are contained in Appendix I. Note that field Nf is simply a
product of field shift factors (SFi) and the estimated lab Nf as described in Chapters 4 through 7.
For this analysis, 0 months aging at 60 °C (140 °F) was considered equivalent to 0 years, 3
months to 6 years, and 6 months to 12 years, respectively, in terms of HMAC pavement age (52).
Consequently, field Nf is plotted as a function of pavement age, as shown in Figure 10-10.
5.00E+06
y = 2E+07e-0.044x
R2 = 0.8446
y = 2E+07e-0.1484x
R2 = 0.9363
1.0E+05
1.0E+06
1.0E+07
1.0E+08
0 5 10 15 20 25 30
Pavement Age (Years)
Fiel
d N
f
Bryan Yoakum
Figure 10-10(a). Field Nf for PS#1, WW Environment – ME Analysis.
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5.00E+06
y = 1E+08e-0.1169x
R2 = 0.9756
y = 7E+07e-0.2034x
R2 = 0.9986
1.0E+05
1.0E+06
1.0E+07
1.0E+08
1.0E+09
0 5 10 15 20 25 30
Pavement Age (Years)
Fiel
d N
f
Bryan Yoakum
Figure 10-10(b). Field Nf for PS#1, WW Environment – CMSE Analysis.
5.00E+06
y = 1E+08e-0.1129x
R2 = 0.9933
y = 7E+07e-0.2054x
R2 = 0.9975
1.0E+05
1.0E+06
1.0E+07
1.0E+08
1.0E+09
0 5 10 15 20 25 30
Pavement Age (Years)
Fiel
d N
f
Bryan Yoakum
Figure 10-10(c). Field Nf for PS#1, WW Environment – CM Analysis.
Like for the lab Nf, these results indicate a decreasing trend for both mixtures with aging,
and the Yoakum mixture exhibits a high field Nf magnitude at all aging conditions. In fact,
Figure 10-10, indicates an exponentially declining Nf trend with aging for both mixtures, and the
rate of Nf decay is mixture dependent based on the slopes of the exponential trend lines fitted
through the Nf data points. Based on the 5 × 106 design traffic ESALs over a 20 year service life
at 95 percent reliability level, all fatigue analysis approaches indicate inadequate and adequate
theoretical fatigue performance for the Bryan and Yoakum mixture, respectively.
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Mixture Field Nf Results – The M-E Pavement Design Guide Analysis
The mixture field Nf results from the M-E Pavement Design Guide software analysis are
presented in Appendix I as mean values of at least two test specimens. Unlike the ME and
CMSE/CM approaches, these results represent field Nf values that incorporate laboratory-to-field
shift factors and effects of aging over a 20 year design period. Essentially, these field Nf results
represent the number of traffic ESALs that the HMAC pavement structure can carry over a 20
year design life prior to 50 percent fatigue cracking in the wheelpath. Figure 10-11 is an
example of the mixture field Nf results from the M-E Pavement Design Guide software analysis.
6.21E+06
4.71E+06
1.00E+00 5.00E+06 1.00E+07
Yoakum
Bryan
Figure 10-11. Field Nf for PS#1, WW Environment – M-E Design Guide Analysis.
The comparatively higher field Nf values of the Yoakum mixture for PS# 1 under the
WW environment shown in Figure 10-11 are consistent with the predictions made by the other
fatigue analysis approaches. Considering a 20-year design service life with traffic design ESALs
of 5.0 × 106, Figure 10-11 shows that only the Yoakum mixture passes the 50 percent wheelpath
cracking failure criterion at 95 percent reliability level. Among other factors, the research team
attributed the comparatively better performance of the Yoakum mixture in terms of higher field
Nf values to the higher binder content in the mixture. Note that binder content is a direct input
parameter in the M-E Pavement Design Guide software, and therefore, field Nf can be tied
directly to this parameter.
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DEVELOPMENT OF A CMSE-CM SHIFT FACTOR DUE TO AGING
As part of this project’s secondary objective, an attempt was made to develop a shift
factor (SFag) that accounts for binder oxidative aging when predicting mixture field Nf using the
CMSE and CM approaches. This section discusses the SFag development based on the binder
dynamic shear rheometer tests that were conducted by CMAC. The CMSE and CM field Nf
predictions using the developed SFag and field Nf at 0 months are also provided.
Theoretical Basis and Assumptions
In this analysis, the SFag was solely based on neat binder shear properties and the
following assumptions, where neat binder refers to binder not mixed with aggregate but that
directly aged in thin films:
• SFag was considered as a multiplicative factor that tends to reduce Nf , and therefore, its
magnitude was postulated to range between 0 and 1 (0 < SFag ≤ 1). A numerical SFag
value of 1 represents unaged conditions or no consideration of aging effects in Nf
analysis.
• SFag was only considered as a function of the neat binder properties in terms of the DSR
function (DSRf) and oxidative aging period (time). The hypothesis is that only the binder
in the HMAC mixture ages, and therefore, it is not unreasonable to determine SFag solely
based on binder properties. The idea is that researchers and/or end-users would only
measure unaged and aged binder properties without having to measure aged mixture
properties and thereafter estimate SFag and ultimately predict aged mixture field Nf from
unaged mixture field Nf.
• The DSRf was utilized on the hypothesis that this function provides a better representation
of the binder shear properties in terms of ductility and durability, properties that are
considered critical to fatigue performance for aged HMAC field pavements (52). The
DSR function’s correlation with ductility, durability, and HMAC pavement age is
discussed in Chapter 8 of this report.
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• The binder oxidative aging conditions as conducted by CMAC were consistent with the
stirred air flow test and pressure aging vessel (PAV*) procedures to simulate both short-
term aging that occurs during the hot-mixing process and construction operations and
long-term aging during service (97). These laboratory aging conditions were SAFT +
PAV* 0 hrs, SAFT + PAV* 16 hrs, and SAFT + PAV* 32 hrs, respectively, and simulate
approximately up to 6 years of Texas field HMAC aging exposure (52,97).
• In contrast to SAFT + PAV* laboratory aging of binders, field aging is a relatively
complex process involving fluctuating environmental conditions and a general decreasing
AV content due to traffic compaction. These factors were not directly taken into account
by the SFag developed in this study. It must also be emphasized that the effect of aging on
HMAC mixture fatigue resistance is considered as a three stage process involving binder
oxidation, binder hardening, and mixture field Nf decay. Additionally, mixture design
parameters such as binder content and polymer modification probably also play a
significant role in these three processes.
SFag Formulation and the Binder DSR Master-Curves
In this project, the SFag was formulated as a function of the DSR data from the binder
DSR master-curve, as shown by Equation 10-5.
[ ]w
ag tuSF )(χ= (Equation 10-5)
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
if
fi
tDSRtDSR
tmtm
t@@
@'@'
)()1(
0)1(
0
χ (Equation 10-6)
( )[ ]'/'/' GGDSRf η= (Equation 10-7)
( ) '
)1()( mff DSRDSR ϖϖ = (Equation 10-8)
where:
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190
SFag = Shift factor due to binder oxidative aging
χ(t) = Material property ratio that relates the aged to the unaged binder shear
properties as a function of time
u, w = Material regression constants
m′ = Slope of the binder DSRf ( ω) master-curve at a reference temperature of
20 °C (68 °F)
ϖ = Reduced angular frequency (rad/s)
DSRf(1) = ( )[ ]'/'/' GG η at 1 rad/s (Pa⋅s)
G’ = Elastic dynamic shear modulus (MPa)
η’ = Dynamic viscosity (Pa⋅s)
Figure 10-12 is a plot of the binder DSR master-curves on a log-log scale in the form of a
power function expressed by Equation 10-8. These binder DSR master-curves were generated
from DSR test data that were measured at three test temperatures of 20, 40, and 60 °C (68, 104,
and 140 °F), respectively within an angular frequency of 0.1 to 100 rad/sec. For analysis
simplicity, SAFT+PAV* 0 hr was assumed to be equivalent to 1 year Texas field HMAC
exposure, SAFT+PAV* 16 hrs to 2 years, and SAFT+PAV* 32 hrs to 6 years, respectively
(52). The SFag at 0 years field HMAC exposure was arbitrary assigned a numerical SFag value of
1.0 on the premise that no significant aging occurs during this period. Based on the data from
Figure 10-12 and using Equation 10-5 (with u ≅ w ≅ 1), SFag values were estimated as a function
of pavement age, as shown in Table 10-8.
Table 10-8. CMSE-CM SFag Values.
SFag Pavement Age (Years) PG 64-22 (Bryan) PG 76-22 (Yoakum)
0 1.000 1.000 1 0.854 0.783 2 0.330 0.303 6 0.160 0.221 12 0.073 0.109 18 0.049 0.081 20 0.045 0.070
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PG 64-22
y = 714860x2.0777
R2 = 0.9923
y = 2E+06x1.9256
R2 = 0.9936
y = 4E+06x1.8613
R2 = 0.9942
1.0E-08
1.0E-05
1.0E-02
1.0E+01
1.0E+04
1.0E+07
1.0E+10
1.0E+13
1.0E-06 1.0E-04 1.0E-02 1.0E+00 1.0E+02w (rad/s)
DS
Rf (P
a.s)
SAFT+PAV 0hrs SAFT+PAV 16hrs SAFT+PAV 32hrs
PG 76-22
y = 1E+06x1.9851
R2 = 0.9952
y = 3E+06x1.795
R2 = 0.9983
y = 4E+06x1.7519
R2 = 0.9987
1.0E-08
1.0E-05
1.0E-02
1.0E+01
1.0E+04
1.0E+07
1.0E+10
1.0E+13
1.0E-06 1.0E-04 1.0E-02 1.0E+00 1.0E+02
w (rad/s)
DSR
f (Pa
.s)
SAFT+PAV 0hrs SAFT+PAV 16hrs SAFT+PAV 32hrs
Figure 10-12. Binder DSRf(ω) Master-Curves at 20 °C (68 °F).
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Note that SFag values beyond 6 years field HMAC exposure were determined based on
the SAFT+PAV* 0 hrs, SAFT+PAV* 16 hrs, and SAFT+PAV* 32 hrs data. Additional
laboratory aging conditions are recommended, i.e., SAFT+PAV* 64hrs that may be realistically
close to a 20 year field HMAC exposure, which is consistent with typical HMAC pavement
design periods.
CMSE-CM Field Nf Prediction Using SFag
Using the SFag data in Table 10-8 and the field Nf at 0 years field HMAC exposure, the
field Nf at any pavement age can be estimated using the following relationship:
( ) ( ) ( )0 tftagtfNFieldSFNField
ii×= (Equation 10-9)
Table 10-9 provides an example of the estimated field Nf at year 20 for PS#1 and the WW
environment. Predictions for other PSs and the DC environment are contained in Appendix I.
Table 10-9. Example of Field Nf Predictions at Year 20 (PS#1, WW Environment).
Approach Mixture Field Nf Value @ Year 20
Bryan 3.11 × 106 CMSE Yoakum 8.40 × 106 Bryan 3.10 × 106 CM Yoakum 7.77 × 106
Design traffic ESALs over 20 year design period at 95 percent reliability level: 5.00 × 106
From Table 10-9, the field Nf estimate by the two approaches do not differ significantly.
In fact, both approaches indicate inadequate and adequate theoretical fatigue performance for
Bryan and Yoakum mixtures, respectively, based on a 5.00 × 106 design traffic ESAL over a
20-year design period at 95 percent reliability level. For this pavement structure (PS#1), these
results are comparable to the predictions by the M-E Pavement Design Guide of 4.71 × 106 and
6.21 × 106 for the Bryan and Yoakum mixtures, respectively. For the ME approach, the
predictions are approximately 1.03 × 106 and 8.30 × 106 for the Bryan and Yoakum mixture,
respectively, based on extrapolations and the exponential relationships in Figure 10-10(a).
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SUMMARY
In this chapter, the HMAC mixture results were presented and the following summarizes
the key findings (based on the test conditions considered in the project).
BB Testing
• The number of laboratory load cycles to failure denoted as N (without subscript f )
decreased with binder oxidative aging.
• The Yoakum mixture performed better in terms of the number of N to failure during BB
testing at 20 °C (68 °F).
Tensile Stress
• Due to more brittle behavior with binder oxidative aging, the mixture tensile failure strain
(εf) at break under tensile loading at 20 °C (68 °F) decreased significantly with aging.
• While the tensile stress at break (σt) did not vary significantly as a function of aging and
was within the expected test variability, the Yoakum mixture exhibited more ductility at
all aging conditions compared to the Bryan mixture.
• With aging, the failure mode under tensile loading for each mixture changed from ductile
to brittle, indicating a decrease in mixture ductility with aging.
Relaxation Modulus
• While the mixture elastic relaxation modulus (E1) increased with binder oxidative aging
due to stiffening effects, the RM results indicated that the Yoakum mixture had a better
potential to relax stress than the Bryan mixture based on a larger m value. However, as
expected, the ability to relax the stress (m value) generally decreased with aging for both
mixtures.
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• Although designed with a relatively softer PG 64-22 binder, the relaxation modulus (E1)
of the Bryan mixture was relatively higher than that of the Yoakum mixture designed
with a stiffer SBS modified PG 76-22 binder, particularly after aging. These results are
suggestive that for the test conditions considered in this project, the Bryan mixture was
perhaps more susceptible to stiffness age-hardening due to binder oxidative aging.
• The logarithm of the temperature shift factor (Log aT) determined when generating the
RM master-curves exhibited a linear relationship with temperature, but this parameter
was insensitive to binder oxidative aging conditions. By contrast, Log aT exhibited some
degree of sensitivity to HMAC mixture type.
DPSE and SE Results
• The DPSE results indicated that the Bryan mixture was more susceptible to fracture
damage than the Yoakum mixture, and the rate of fracture damage accumulation
generally increased with aging.
• The SE results indicated better adhesive bond strength for the Yoakum mixture relative to
the Bryan mixture, and mixture resistance to fracture and potential to heal as measured in
terms of SE magnitude generally decreased with aging.
Mixture Anisotropy
• Within a ±15 percent error tolerance, mixture anisotropy (SFa) was observed to be
insignificantly affected by binder oxidative aging and did not vary substantially as a
function of mixture type. Consequently, a mean SFa value of 2.0 was proposed for both
the Bryan and Yoakum mixtures for all aging conditions.
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Mixture Nf
• When comparing the two mixtures for the test conditions considered in this project:
The Yoakum mixture exhibited better fatigue resistance than the Bryan mixture in
terms of the magnitude of both lab and field Nf .
The Yoakum mixture was more resistant to fracture damage, had a better potential to
heal, and was less susceptible to aging compared to the Bryan mixture.
• An attempt was made to develop shift factors due to aging (SFag) based on the binder
DSR function for the CMSE and CM approaches. While the SFag methodology utilized
produced reasonable results, validation of these concepts is still required through testing
of additional binders and HMAC mixtures, possibly with longer laboratory aging periods
that realistically simulate current HMAC pavement design practices. The further
development of representative SFag, particularly as a function of time, with more research
will inevitably allow for realistic Nf predictions at any desired pavement age.
Furthermore, there is a need to incorporate mixture volumetric properties such as AV and
binder content in the SFag model. These volumetric properties are hypothesized to play a
significant role in the aging phenomenon of HMAC mixtures due to binder oxidation.
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CHAPTER 11 DISCUSSION AND SYNTHESIS OF RESULTS
This chapter compares and discusses the mixture field Nf results and variability including
the effects of other input variables, and binder oxidative aging. BM characterization and another
proposed methodology for the aging shift factor (SFaging) analysis for the CMSE approach are
also discussed.
COMPARISON OF MIXTURE FIELD Nf
Generally, all fatigue analysis approaches predicted higher Nf (both lab and field) values
for the Yoakum mixture under all aging and environmental conditions for all pavement
structures. Mixture property results discussed in Chapter 10 also indicated that the Yoakum
mixture had better fatigue resistant properties than the Bryan mixture and was therefore expected
to perform better in terms of Nf (lab or field) magnitude under the test conditions considered in
this project. Figure 11-1 is an example of the mixture field Nf for WW environmental conditions
for PS# 1.
1.0E+051.0E+061.0E+071.0E+081.0E+09
Field Nf
ME CMSE CM
BryanYoakum
Figure 11-1(a). Mixture Field Nf (0 Months, PS#1, WW Environment).
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1.0E+051.0E+061.0E+071.0E+081.0E+09
Field Nf
ME CMSE CM
BryanYoakum
Figure 11-1(b). Mixture Field Nf (3 Months, PS#1, WW Environment).
1.0E+051.0E+06
1.0E+071.0E+081.0E+09
Field Nf
ME CMSE CM
BryanYoakum
Figure 11-1(c). Mixture Field Nf (6 Months, PS#1, WW Environment).
Figure 11-1(a) represents field Nf values that were measured at 0 months with no
aging effects being considered. The 3 and 6 months field Nf results for the ME, CMSE, and CM
approaches in Figures 11-1(b) and (c) represent approximately 3 to 6 years of field aging (52).
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Figures 11-1(a), (b), and (c) show better fatigue resistance for the Yoakum mixture in
terms of field Nf magnitude. Note that the difference (Figure 11-1) in the field Nf values between
the two mixtures gets more significant as aging progresses, indicating that the Bryan mixture’s
fatigue life was decaying much faster than that of the Yoakum mixture. This result is consistent
with the material property results reported in Chapter 10.
The M-E Pavement Design Guide results represent field Nf values at year 20 and
incorporates laboratory-to-field shift factors and effects of aging through the GAM over the
entire 20 year design period and were not included in Figures 11-1(a), (b), and (c). These M-E
Pavement Design Guide results are included in Figure 11-1(d), which is an example of the
mixture field Nf prediction comparison based on a 20-year design life and 95 percent reliability
level for PS# 1 under the WW environment.
0.0E+00 5.0E+06 1.0E+07
Field Nf
ME
CMSE
CM
Design Guide
Bryan Yoakum
Figure 11-1(d). Mixture Field Nf Comparison (PS#1, WW Environment)
For all the fatigue analysis approaches, Figure 11-1(d) shows better fatigue resistance for
the Yoakum mixture in terms of field Nf magnitude compared to the Bryan mixture. Based on the
5 × 106 design traffic ESALs and 20 years service life at 95 percent design reliability level for
this pavement structure and the environmental conditions under consideration, all the fatigue
analysis approaches (although with different failure criteria) indicate inadequate and adequate
theoretical fatigue performance for the Bryan and Yoakum mixtures, respectively.
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Considering that the Yoakum mixture was designed with a relatively stiffer SBS
modified PG 76-22 binder, this relatively better fatigue performance in terms of field Nf results
was theoretically unexpected. In fact, the theoretical expectation was that the Yoakum mixture’s
fatigue performance in terms of field Nf magnitude would be worse compared to the Bryan
mixture. However, the research team attributed this response behavior to the following factors:
• Compared to the Bryan mixture, the Yoakum mixture had relatively higher binder
content (5.6 percent versus 4.6 percent by weight of aggregate).
• Contrary to theoretical expectations based solely on stiffness alone, the SBS modifier
probably improved the Yoakum mixture’s fatigue resistance as well as reduced its
susceptibility to binder oxidative aging.
• The Yoakum mixture incorporated a 1 percent hydrated lime in the mixture design.
Although lime is often added to improve mixture resistance to moisture damage, this lime
perhaps increased the mixture’s resistance to both fatigue damage and aging. Wisneski et
al. made similar observations that lime tended to improve the performance of recycled
asphalt (114).
• SE results in Chapter 10 indicated a better fracture resistance and stronger potential to
heal for the Yoakum mixture than for the Bryan mixture. Based on these SE results, it can
be theorized that the PG 76-22 binder-gravel aggregate has an increased bond strength
compared to that of the PG 64-22 binder-limestone aggregate combination. Note that one
of the SE measurements’ objectives is often to asses the affinity and bond (cohesive
and/or adhesive) strength of binders and aggregates. Theoretically, a comparatively
better bond strength compatibility between the binder and aggregate (in this case for the
Yoakum mixture) is generally expected to exhibit superior performance.
• Tensile strength and RM results in Chapter 10 indicated that the Yoakum mixture was
more ductile and less susceptible to stiffness age-hardening compared to the Bryan
mixture, properties which probably contributed to its higher field Nf values. Additionally,
the Yoakum mixture exhibited better potential to relax the stress, as indicated by higher
m values, compared to the Bryan mixture.
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Although theoretically possible, the research team considers that it may be inappropriate
and/or rather complex to make a direct comparison between these two mixtures because their
mix-design characteristics (binder content, aggregate type and gradation) and materials (the
aggregates) were different. Therefore, because of the many existing variable parameters, the
comparison of these two HMAC mixtures may be inconclusive.
Overall, these results, however, suggests that binder stiffness or initial mixture stiffness
alone may not be used as the sole determinant or measure of HMAC mixture fatigue resistance
or field fatigue performance. A mixture designed with a stiffer binder may not necessarily imply
that it will perform poorly in fatigue compared to a mixture designed with a softer binder. The
entire mix-design matrix and spectrum of material properties need to be evaluated, particularly in
performance comparison studies of this nature. Equally to be considered is the pavement
structure, the environmental conditions, and the mixture sensitivity to aging in terms of binder
oxidation and stiffness age-hardening rate and probably even the binder’s potential to heal.
MIXTURE VARIABILITY
As observed in Chapter 10, there was generally a high variability in the Yoakum mixture
results, both in terms of mixture properties and field Nf results (COV of Ln Nf). Compared to the
Bryan mixture, the Yoakum mixture consists of a stiffer SBS modified PG 76-22 binder that is
relatively harder to work with when mixing, compacting, and sawing/coring. Table 11-1 shows
an example of the mixture AV variability.
Table 11-1. Example of HMAC Specimen AV Variability.
Specimen Mixture Target AV Average AV Stdev COV
Bryan 7±0.5% 7.23% 0.20 2.81%Cylindrical
Yoakum 7±0.5% 7.10% 0.35 5.94%
Bryan 7±0.5% 7.18% 0.29 4.04%Beam
Yoakum 7±0.5% 6.98% 0.55 7.87%
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Table 11-1 represents the average AV content of 10 random sample specimens per
specimen type per mixture type. Although the COV values are reasonably acceptable, Table 11-1
clearly shows the high variability in the AV content for the Yoakum mixture. Modified binders
are generally more difficult to work with, and consequently, it is more difficult to control the AV
content, which was ultimately reflected in the high variability of the final results. For this
Yoakum mixture, the other compounding factor may have been the higher binder content. Not
only was the PG 76-22 binder stiffer and difficult to work with, its content in the mixture was
also higher relative to the PG 64-22 of the Bryan mixture.
From Table 11-1, it is also worthwhile to note the relatively high variability in the AV for
the beam specimens. In this project, it was generally more difficult to control the AV for the
beam specimens during compaction due to the nature of their shape and the kneading compaction
method. This high variability in the AV content was also reflected in the final ME lab Nf results
discussed in Chapter 10 and the field Nf results shown in Table 11-2. The cylindrical specimens,
on the other hand, are compact and easy to handle, and the gyratory compaction method allows
for better control of the AV content.
Mixture field Nf results generally indicated higher variability with the Yoakum mixture
and for the ME approach for all PSs, environmental, and aging conditions. Table 11-2 gives a
summary example of the mixture field Nf statistical analysis in terms of the COV of Ln Nf and the
95 percent CI for PS#1 and WW environment based on a 20-year design period.
Table 11-2. Example of Mixture Field Nf Variability (PS#1, WW Environment).
Field Nf Approach Mixture
Mean Value COV of Ln Nf 95% CI
Bryan 1.03 × 106 6.87% 0.49 – 2.17 × 106
ME Yoakum 8.30 × 106 9.85% 5.41 – 16.74 × 106
Bryan 3.11 × 106 2.81% 3.08 – 3.21 × 106
CMSE Yoakum 8.40 × 106 3.92% 6.95 – 9.82 × 106
Bryan 3.10 × 106 2.93% 2.98 – 4.47 × 106
CM Yoakum 7.77 × 106 3.98% 6.12 – 8.08 × 106
Bryan 4.71 × 106 ------- 1.93 – 9.74 × 106M-E Design Guide Yoakum 6.21 × 106 ------- 2.04 – 15.34 × 106
Design traffic ESALs over 20 year design period at 95 percent reliability level: 5.00 × 106
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From Table 11-2, it is evident that variability in terms of COV of Ln Nf and 95 percent CI
is relatively higher for the Yoakum mixture. These COV values seem low because they are
expressed in terms of logarithmic response, which provides a better statistical analysis in terms
of an assumed normal distribution. However, they nonetheless provide a comparative basis for
the approaches. Note that no COV of Ln Nf values are reported for the M-E Pavement Design
Guide in Table 11-2. This is due to the nature of the back-calculation analysis of field Nf at 50
percent cracking using percentage cracking output values from the M-E Pavement Design Guide
software. The Nf backcalculation analysis does not allow for a realistic determination of
representative COVs. Although three specimens were used for each mixture, the output is just
one single field Nf value.
From Table 11-2, it is clearly evident that the ME exhibited the highest statistical
variability, both in terms of the COV values and 95 percent CI range (particularly for the
Yoakum mixture with the modified binder). The CMSE, in contrast, exhibited the least statistical
variability as measured in terms of the COV values of Ln Nf and 95 percent CI range.
EFFECTS OF OTHER INPUT VARIABLES ON MIXTURE FIELD Nf
Among other variables, mixture fatigue performance is dependent on the pavement
structure and environment. The effect of these variables on mixture field Nf and fatigue
performance assuming similar traffic loading conditions are discussed in this section.
Pavement Structure
HMAC mixture field Nf prediction and fatigue performance is a function of the strain
(tensile or shear) as the failure load-response parameter. For any given pavement structure
(assuming similar traffic loading and environmental conditions), the critical maximum design
strain is computed as a function of the number of structural layers, layer thicknesses, and the Ei
and ν values of the respective layers. Figure 11-2 is an example of the effect of pavement
structure on the mixture field Nf under WW environmental conditions based on a 20 year design
period for the Bryan mixture. Structural details of the pavement structures (PS# 1, PS# 4, and
PS# 5) shown in Figure 11-2 are summarized in Table 3-7.
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1.0E+05
1.0E+06
1.0E+07
1.0E+08
Field Nf
PS#4 PS#1 PS#5
MECMSE
CMM-E Design Guide
Figure 11-2. Effect of Pavement Structure on Mixture Field Nf
(Bryan Mixture, WW Environment).
In terms of fatigue analysis, the optimum combination of the number of layers, layer
thicknesses, and Ei values that gives the lowest critical maximum design strain will result in
higher field Nf value and better fatigue performance in the field. Because fatigue cracking
initiates due to horizontal tensile and/or shear strains in the HMAC layer that exceed the capacity
of the HMAC, pavement structures with higher values of the critical maximum design strain will
generally be more susceptible to fatigue cracking than those with lower values.
PS# 5 in Figure 11-2 has the least critical maximum design strain (Table 3-7) and
therefore highest field Nf values for all the fatigue analysis approaches. According to Table 3-7,
PS# 1 and 5 are three-layered pavement structures (including the subgrade), while PS# 4 is
four-layered. However, the relatively 4 inch thick HMAC layer in PS# 5 is resting on a stiff
cemented base that provides support for the loading and produces lower strains in the top HMAC
layer, and subsequently higher field Nf values.
Ultimately, these results demonstrate the inseparable nature of pavement structural design
and HMAC mix-design for fatigue resistance. HMAC mixture fatigue resistance cannot be
modeled explicitly without consideration of a representative field pavement structure.
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Environmental Conditions
As discussed in Chapters 2 and 3, environmental conditions have a significant effect on
the pavement material properties in terms of the Ei values. These Ei values, in turn, have an
effect on the design strain that ultimately has an effect on Nf. Figure 11-3 shows the effect of
environmental conditions for PS# 1 based on the M-E Pavement Design Guide analysis that
incorporates a very comprehensive climatic analysis model.
WWDC
Bryan
Yoakum1.0E+06
1.0E+07
Field Nf
Figure 11-3. Effect of Environmental Conditions on Mixture Field Nf (PS#1).
From Figure 11-3, both mixtures exhibited relatively higher field Nf values in the DC
environment. The lower field Nf values in the WW environment are possibly due to the wetting
effect (presence of moisture) that had a significant effect on the Ei values of the unbound
pavement layers, including the subgrade. Note that the presence of moisture within and/or
underneath a PS is to reduce the Ei value that ultimately results in a higher εt value in the HMAC
layer.
Overall, these results indicate that HMAC mixture fatigue resistance is pavement
structure and environmental location dependent. The results signify the importance of adequately
interfacing HMAC mix-design and fatigue characterization with pavement structural design and
analysis to achieve adequate field fatigue performance.
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BINDER TEST RESULTS AND EFFECTS OF AGING
Two binders, an unmodified PG 64-22 and a polymer-modified PG 76-22, were used in
this project. Neat binders and binders recovered from laboratory mixtures, at several levels of
aging, were evaluated. Neat binders were aged in a HMAC simulation, the stirred air-flow test,
to give one level of aging. Then these binders were further aged in the 60 °C (140 °F)
environmental room in thin films (approximately 1 mm [0.039 inches] thick) for 3 and 6 months
to obtain a second and third aging level (SAFT+3M and SAFT+6M). For recovered binders,
aging states were obtained by aging two asphalt-aggregate mixtures (designated Bryan and
Yoakum). The mixtures were prepared using the PP2 short-term aging protocol and then
compacted; this method produced one aging level (PP2+0M). The second and third levels were
obtained by aging the compacted laboratory mixture in the environmental room for 3 and 6
months beyond PP2 conditioning (PP2+3M and PP2+6M). Note that the “0 months,” “3
months,” and “6 months” refer to environmental room aging beyond PP2 aging so that 0 months
aging still has a significant level of aging beyond SAFT aging.
The binders in the compacted mixtures were extracted and recovered according to the
procedure outlined in Chapter 8. SEC was used to check whether the solvent residues exist in
the binder. SEC chromatograms for recovered binders from Bryan mixtures are shown in Figure
11-4 and show that the recovered binders did not have solvent residue, which, if present, would
significantly affect the rheological properties. They also show that the asphaltene peak, centered
at about 23 minutes of retention time, increased with aging, a common result.
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-0.20
-0.10
0.0
0.10
0.20
0.30
0.40
0.50
0.60
15 20 25 30 35 40 45
PP2-3MPP2-0M
RI R
ESPO
NSE
RETENTION TIME (minutes)
* 3M- Bryan mix, 3 month aged in 60 oC room*0M- Bryan mix just after it was made
Recovered Bryan
Figure 11-4. SEC Chromatogram for Recovered Binders from Bryan Mixtures
(°F = 32 + 1.8 (°C)).
The aged binders were characterized by DSR and FTIR measurements. Aging increases
carbonyl area (oxygen content), viscosity, and the elastic modulus, but decreases the ductility.
Figures 11-5 and 11-6 are a plot of the CA and zero shear viscosity, respectively, for the Bryan
binder (PG 64-22).
Figure 11-5 shows that CA increases with aging time for neat and recovered binders from
Bryan mixtures. SAFT aging leaves the binder within the initial jump (higher aging rate) region,
whereas PP2 aging is more severe and produces a binder that is past this region. Thus, the three
PP2 data points show a uniform aging rate where as the SAFT points show a higher rate (slope)
between 0 and 3 months than between 3 and 6 months.
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Figure 11-5. CA Rate of Bryan Binder (PG 64-22)
(F = 32 + 1.8(C)).
Figure 11-6. Zero Shear Viscosity Hardening Rate of Bryan Binder (PG 64-22) (F = 32 + 1.8(C)).
0 1 2 3 4 5 6 7 8 90.0
0.5
1.0
1.5
2.0
PP2 + 0, 3, 6M SAFT+ 0, 3, 6M
CA
Aging Time ( months at 60 oC, 1 atm)
Binder for Bryan Mixture
0 1 2 3 4 5 6 7 8 9104
105
106
PP2 + 0, 3, 6M SAFT+ 0, 3, 6M
η* 0(P
oise
, 60
o C, 0
.1 ra
d/s)
Aging Time ( months at 60 oC, 1 atm)
Binder for Bryan Mixture
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209
The zero shear viscosity of the Bryan binder also increases with aging time, and PP2 aged
binder seems to have passed the initial jump period in Figure 11-6, as the data for all three aging
times show the same hardening rate. The DSR function (G’/(η’/G’)) for the Bryan binder, shown
in Figure 11-7, versus the CA, also increases with aging. The DSR function is plotted on a
logarithmic scale against the CA, which represents the amount of aging. Thus, aging time is
removed as a factor, and PP2-aged binder and SAFT-aged binder show the some relation
between CA and DSR function.
Figure 11-7. DSR Function vs. Carbonyl Area of Bryan Binder (PG 64-22)
(°F = 32 + 1.8(°C)).
The Yoakum binder is a polymer modified binder, PG76-22, for which the zero shear
viscosity is not appropriate for characterizing hardening rate (polymer-modified binders typically
do not exhibit a zero shear viscosity). Instead, the DSR function (at a defined temperature and
frequency) hardening rate is used to represent changes of binder physical properties with aging in
Figure 11-8.
0.0 0.5 1.0 1.5 2.010-5
10-4
10-3
10-2
PP2 SAFT before IJ SAFT after IJ
(G'/(
η'/G
')) M
Pa/s
15
o C, 0
.005
rad/
s
CA
Binder for Bryan Mixture Design
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210
The DSR function of the Yoakum binder increases with aging time, and the PP2 aging
process (PP2 + 0M) aged the Yoakum binder more than the SAFT process (SAFT + 0M).
However, after 3 and 6 months additional aging in the 60 oC (140 °F) room, the neat thin-film
aged Yoakum binder was somewhat harder than the mixture aged binder.
The thin film binder catches up with the mixture binder partly because, after SAFT, it is
still in the higher aging-rate initial jump period, but also because binder aging in thin film has
more access to oxygen than binder in compacted mixtures. In the case of the Bryan binder
(Figures 11-5 and 11-6), it appears that the same process is occurring, but the neat binder takes
longer to catch up to the mixture-aged binder. Increase of the CA for the Yoakum binder is
shown in Figure 11-9.
Figure 11-8. DSR Function Hardening Rate of Yoakum Binder (PG 76-22)
(°F = 32 + 1.8(°C)).
0 1 2 3 4 5 6 7 8 910-5
10-4
10-3
10-2
PP2 + 0, 3, 6M SAFT + 0, 3, 6M
(G'/(
η'/G
'))
MPa
/s 1
5 o C
, 0.0
05 ra
d/s
Aging Time ( months at 60 oC, 1 atm)
Binder for Yoakum Mixture
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211
0 1 2 3 4 5 6 7 8 90.5
1.0
1.5
2.0
PP2 + 0, 3, 6M SAFT + 0, 3, 6M
CA
Aging Time ( months at 60 oC, 1 atm)
Binder for Yoakum Mixture
Figure 11-9. CA Rate of Yoakum Binder (PG 76-22)
(°F = 32 + 1.8(°C)).
Figure 11-10 shows the increase in DSR function with CA for the Yoakum binder. Again,
both neat binder and mixture aged binder show the relation, suggesting the same aging
mechanism is followed in both cases.
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212
0.0 0.5 1.0 1.5 2.010-5
10-4
10-3
10-2
PP2 + 0, 3, 6M SAFT + 0, 3, 6M
(G'/(
η'/G
')) M
Pa/s
15
o C, 0
.005
rad/
s
CA
Binder for Yoakum Mixture
. Figure 11-10. DSR Function vs. CA for Yoakum Binder (PG 76-22)
(°F = 32 + 1.8(°C)).
BINDER-MIXTURE CHARACTERIZATION AND AN AGING SHIFT FACTOR
In Chapter 10, the effect of binder oxidative aging on mixture fatigue life was presented.
The decrease in fatigue life with aging is striking, and significant differences in the rate of
decline were noted between the Bryan and Yoakum mixtures. The reasons for these differences
are, as yet, unknown. The discussion in this section elaborates on the possible impact of this
decline in fatigue life on a pavement’s service life. The question addressed is, “What shift factor
should be applied to a pavement’s service life due to binder oxidative aging?”
Another approach, different from the SFag approach discussed in Chapter 10, is presented
in this section. The approach, discussed below, utilizes binder DSR functions and attempts to
incorporate the significant aspect of traffic loading, and is based on field Nf.
First the following definitions are made:
Nf = Field fatigue life, in ESALs, and
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Fraction of Life Expended During Time ( ) /f
dtdtN t RL
=
end
01( ) /
t
f
dtN t RL
=∫
1 20( ) K K t
f fN t N e−=
1 2 0end
1 2
ln( / 1)f LK K N Rt
K K+
=
1 2 0
1 2 0
ln( / 1)Age-shortened LifeUnaged Life Expectancy /
f Laging
f L
K K N RSF
K K N R+
= =
RL = Pavement loading rate, ESALs/yr.
Then Nf / RL = Pavement Fatigue Life Expectancy, in years, is a constant over the life of
the pavement value of field Nf . If, however, field Nf is a function of time (and declines with
binder oxidative aging, e.g.), then this decline must be taken into account when estimating the
pavement fatigue life. For a differential time period dt during which the field fatigue life is Nf(t),
the fraction of a pavement’s total available fatigue life consumed during dt is calculated as:
(Equation 11-1)
Then, Miner hypothesis (18, 115) is used to sum over the pavement’s entire life, defined to be
the amount of time to reach an integrated fraction equal to unity as follows:
(Equation 11-2)
From the experimental data for the decline of field Nf with binder oxidative aging, Nf(t)
can be represented by an exponential relation:
(Equation 11-3)
where K1 is the magnitude of the power law slope that relates the decline of Nf to the increase in
the DSR function G’/(η’/G’) with aging, and K2 is the (exponential) rate of increase of the DSR
function with aging time in the pavement. Solving this integral for tend gives the following
equation:
(Equation 11-4)
An aging shift factor can be defined as the ratio of the age-shortened fatigue life to the
unaged fatigue life expectancy:
(Equation 11-5)
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From this relation, the bigger K1 and K2 are in magnitude; the smaller the aging shift
factor, the shorter the pavement’s fatigue life expectancy. Equation 11-5 also shows that K1 and
K2 have an identical effect on this shift factor. That is, the impact of aging on the DSR function
and the response of the fatigue life to these changes in DSR function produce the same effect on
the final aging shift factor.
The decline of mixture fatigue with increasing DSR function is shown for both the Bryan
and Yoakum mixtures in Figure 11-11. Values of Nf0 (here equal to the fatigue life of the PP2-
aged compacted mixtures) were reported in Chapter 10, and K2, the ln (DSR function) hardening
rate, is taken from a lab-to-field hardening rate conversion obtained in Project 0-1872
(Table 9-8) (52) and applied to the DSR function hardening rate (Figure 11-12). Hardening
rates, of course, vary from pavement to pavement and depend principally upon the climate, but
also, and perhaps to a lesser degree, on air voids and binder content. Consequently, the value
used here gives only a very approximate indication for any specific pavement.
10-4 10-3 10-2106
107
108
109
For Bryan Field Nf: y = a*x̂ b R^2 = 0.994a 664b -1.37
For Yoakum Field Nf: y = a*x̂ b R^2 = 0.998a 71100b -0.908
YKM-Nf(CMSE) (Field) BRY-Nf(CMSE) (Field)
Mix
ture
Fie
ld N
f
Binder ( G'/( η'/G') ) MPa/s, 15 oC, 0.005 rad/s
IncreasingAging
Field Nf vs Binder DSR Function
Figure 11-11. Decline of Mixture Nf with Binder DSR Function Hardening
(°F = 32 + 1.8(°C)).
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215
Figure 11-12. DSR Function Hardening Rate of Neat Binder after Initial Jump
(°F = 32 + 1.8(°C)).
Table 11-3 summarizes the parameters and calculations for the two mixtures. A loading
rate of 3 million ESALS/yr was arbitrarily selected for these calculations. This number is high,
perhaps corresponding to a heavily traveled freeway in a major city. A lower number will give
longer fatigue lives. These calculations are intended only to represent a calculation procedure
that shows the differences in fatigue life that might be expected between different mixtures,
based upon laboratory measurements that take into account binder oxidative aging. More
laboratory and field data are needed to verify this approach.
Table 11-3. Summary of Pavement Fatigue Life Parameters.
Mixture Nf0 1 ×106 ESALs
RL 1 ×106 ESALs/Yr
K1 K2 SFaging Pavement
Fatigue Life (Yrs after PP2)
Bryan 69 3 1.37 0.26 0.27 6.2Yoakum 120 3 0.91 0.16 0.33 13.2
10-4
10-3
10-2
0 1 2 3 4 5 6 7
BRY-SAFT+3, 6M
YKM-SAFT+3, 6M
y = 0.00011697 * e^(0.32638x)
y = 0.00048389 * e^(0.20036x)
Aging Time (months at 60 oC, 1 atm)
(G'/(
η'/G
')) M
Pa/s
, 15
o C, 0
.005
rad/
s
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216
The calculated shift factors are markedly different, and the differences in the estimated
pavement fatigue life (after PP2 short-term aging) results for the two mixtures are striking. It
should be noted again that the PP2 short-term aging produces a binder in the mixture that is
significantly more aged than the SAFT (RTFOT equivalent) aged binder. How PP2 aging
compares to the aging of an in-service HMAC pavement is yet unknown. However, based upon
SH 21 data, reported in Project 0-1872 (52), the PP2 aging may reflect as much as 4 years of
HMAC pavement in-service life. If so, the 6 years after PP2 (Bryan mixture) amounts to 10
years HMAC pavement total service life, and the 13 years after PP2 for the Yoakum mixture
would correspond to 17 years of HMAC pavement total service life.
The differences in aging shift factors and pavement fatigue lives for the two mixtures are
the results of K1 , the rate at which the fatigue life declines with oxidative hardening of the
binder and K2, the binder’s hardening rate in the pavement. This is seen dramatically in Figures
11-13 through 11-15.
Figure 11-13. Calculated Decline of Remaining Pavement Fatigue Service Life.
0 5 10 15 20 25 30 35 400.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Shift Factor=0.33
Rem
aini
ng F
ract
ion
of S
ervi
ce L
ife
Service Time after PP2(4-hr)-Level Aging (year)
Bryan Mixture- With Aging Bryan Mixture- Without Aging Yoakum Mixture- With Aging Yoakum Mixture- Without Aging
The Effect of Oxidative Aging on Estimated Pavement Fatigue Life
Bryan: Nfo = 69x106 ESALs K1 =1.37; K2 = 0.26; RL = 3x106 ESALs/yrYoakum: Nfo = 120 x106 ESALS K1 = 0.91; K2 = 0.16; RL = 3x106 ESALs/yr
Shift Factor=0.27
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Figure 11-13 shows the decline of the remaining fatigue life with service time (after PP2
aging), determined by integrating Equation 11-2 for times shorter than tend. Both the Bryan and
Yoakum mixtures are shown, and the straight-line decline assumes that there is no decline in
fatigue life with aging. Without aging, the Yoakum mixture has a longer service life than the
Bryan mixture due to its initially higher fatigue life (120 versus 69 million ESALs). With binder
oxidative aging, the difference remains, and one might reasonably assume this difference is also
because of the different initial fatigue lives.
Figure 11-14 shows a hypothetical calculation with the Bryan mixture the same, but the
hypothetical case for the Yoakum mixture is the same except that the initial fatigue life is nearly
the same as the Bryan mixture (not identical so both straight-line depreciations can be
identified). While the initial fatigue lives are the same, the shift factors, and thus the service
lives, are significantly different.
Figure 11-14. Hypothetical Decline of Pavement Fatigue Service Life,
Initial Fatigue Lives Equal.
0 5 10 15 20 25 30 35 400.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Bryan: Nfo = 69x106 ESALs K1 =1.37; K2 = 0.26; RL = 3x106 ESALs/yrYoakum: Nfo = 71 x106 ESALS K1 = 0.91; K2 = 0.16/yr; RL = 3x106 ESALs/yr
Shift Factor=0.43
Rem
aini
ng F
ract
ion
of S
ervi
ce L
ife
Service Time after PP2(4-hr)-Level Aging (year)
Bryan Mixture- With Aging Bryan Mixture- Without Aging Yoakum Mixture- With Aging Yoakum Mixture- Without Aging
The Effect of Oxidative Aging on Estimated Pavement Fatigue Life
Shift Factor=0.27
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A second hypothetical case (Figure 11-15) changes the values of K1 and K2 but leaves the
initial fatigue life the same as for the Yoakum mixture. Now, the conclusion is that the initial
difference in fatigue life has minimal impact on the service life, but the rate of decline of fatigue
life with binder hardening has a very profound impact. This conclusion is tentative as the
amount of data is sparse with only two mixtures. Nevertheless, the results are compelling that
the effect of binder oxidative aging in mixtures can have an extremely significant impact on the
pavement service life in terms of fatigue performance.
Additional comments about pavement aging are appropriate. The above data suggest that
when binder aging occurs in the pavement, it can have a very significant impact on pavement
service life in terms of fatigue performance. However, it does not address whether or not binders
in pavements actually age. At least one report in the literature is used to support the idea that
pavements age primarily near the surface and very little more than an inch below the surface
(116). If this is the case, then the issue of the effect of binder oxidative aging on fatigue may be
of little importance.
On the other hand, a recent TxDOT report (52) provides considerable pavement
recovered binder data that support the notion that binders, in fact, do age in HMAC pavements at
depths up to several inches (at least six) and at rates that appear to be minimally abated by depth.
If this is the case, then the impact of binder oxidative aging on HMAC pavement fatigue
performance is of considerable importance and should be considered when designing HMAC
pavements.
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0 5 10 15 20 25 30 35 400.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Bryan: Nfo = 69x106 ESALs K1 =1.37; K2 = 0.26; RL = 3x106 ESALs/yrYoakum: Nfo = 120 x106 ESALS K1 = 1.37; K2 = 0.26; RL = 3x106 ESALs/yr
Shift Factor=0.19
Rem
aini
ng F
ract
ion
of S
ervi
ce L
ife
Service Time after PP2(4-hr)-Level Aging
Bryan Mixture- With Aging Bryan Mixture- Without Aging Yoakum Mixture- With Aging Yoakum Mixture- Without Aging
The Effect of Oxidative Aging on Estimated Pavement Fatigue Life
Shift Factor=0.27
Figure 11-15. Hypothetical Decline of Pavement Fatigue Service Life, Ki Values Equal.
SUMMARY
Key points from a discussion and synthesis of the results are summarized as follows:
• The Yoakum mixture exhibited higher field Nf values compared to the Bryan mixture. This
was probably due to the higher SBS modified binder content and the lime in the mixture. By
contrast, the Yoakum field Nf results exhibited higher variability in terms of the COV of Ln
Nf and the 95 percent CI.
• While the Yoakum mixture exhibited better fatigue performance in terms of the field Nf
magnitude in all the analysis approaches, the mixture field Nf also depends on the following
input variables; pavement structure and environmental conditions.
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• While certain HMAC mixtures may perform satisfactorily well in a particular pavement
structure and environmental location, it may not be true when these variables (pavement
structure and environmental location) are changed.
• For the test protocols and conditions considered in this project, binder test results, when
analyzed as a function of oxidative aging, indicated that:
Aging increases the carbonyl area (oxygen content), DSR function, viscosity, and
elastic modulus.
Aging decreases both binder and mixture ductility.
CA correlates linearly with the DSR function.
AASHTO PP2 4 hrs short-term oven aging has a greater oxidative aging impact on
the binder than SAFT aging. This was evident through the absence of the initial jump
periods in the CA rates of extracted binders from mixtures subjected to AASHTO
PP2 4 hrs short-term oven aging as well as the higher level of aging after the PP2
procedure compared to SAFT aging.
• An approach for developing shift factors due to aging, denoted as SFaging (to differentiate
it from the SFag approach), was developed that includes both binder hardening due to
oxidative aging and decline in fatigue life due to binder hardening. This approach
produced an expected pavement fatigue life in years, based upon an assumed ESALs/yr
loading rate. The impact on fatigue life of binder hardening due to oxidation was
dramatic, and the SFaging results indicated that the Bryan mixture was more susceptible to
decline in fatigue life due to aging than was the Yoakum mixture.
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CHAPTER 12 COMPARISON AND SELECTION OF THE
FATIGUE ANALYSIS APPROACH
This chapter presents the comparative evaluation of the fatigue analysis approaches,
including the selection criteria and the selected and recommended fatigue analysis approach.
COMPARATIVE REVIEW OF THE FATIGUE ANALYSIS APPROACHES
Table 12-1 is a summary comparison of the four fatigue analysis approaches in terms of
laboratory testing, equipment, input data, data analysis, failure criteria, and variability of the
results. Tables 12-1(c) and (d) represent field Nf predictions based on a 20-year design period
with aging effects considered. Only Bryan results are given for the corresponding actual field
section PS#5. Statistical analysis for these approaches was based on least squares regression and
typical spreadsheet descriptive statistics tools discussed in Chapters 4 through 7.
Table 12-1(a). Summary Comparison of the Fatigue Analysis Approaches.
Fatigue Analysis Approach Item
Design Guide ME CMSE/CM
Concept Mechanistic-empirically based
Mechanistic-empirically based
Continuum micromechanics & fundamental HMAC properties
Laboratory testing
Easy but lengthy temperature conditioning time
Rigorous & lengthy Numerous but easy to run & less costly (no SE for CM approach)
Testing time ≅ 5 hrs ≅ 30 hrs ≅ 70 hrs (≅ 5 hrs for CM approach)
Equipment cost*
≅ $130,000 (minus the software)
≅ $155,000 (≅ $25,560 for BB device)
≅ $210,000 (≅ $80,000 for SE devices)
Input data Comprehensive/flexible Comparatively few Comprehensive (no SE for CM approach)
COV of input data ≅ 5% - 23% ≅ 5% - 28% ≅ 4% - 12%
Failure criteria
50% cracking in wheelpath
50% reduction in flexural stiffness
7.5 mm microcrack growth & propagation through HMAC layer
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Table 12-1(b). Summary Comparison of the Fatigue Analysis Approaches.
Fatigue Analysis Approach Item
Design Guide ME CMSE/CM
Analysis procedure Comprehensive Relatively easy &
straightforward Comprehensive & lengthy
Analysis time** ≅ 4.5 hrs ≅ 3 hrs ≅ 6 hrs (≅ 5 hrs for
CM) Mechanistic failure load-response parameter
Maximum critical design tensile strain (εt) @ bottom of HMAC layer
Maximum critical design tensile strain (εt) @ bottom of HMAC layer
Maximum critical design shear strain (γ) @ edge of loaded tire
Fatigue model ( ) ( ) 3322
11kk
tffff EkN ββεβ −−= ( )[ ]2
1k
tf kSFN −= ε ( )
( ) 21
kp
pif
kN
NNSFN−=
+=
γ
Aging effects
Software incorporates a Global Aging model
None (but can possibly use Miner’s hypothesis)
Shift factor (SFag) being developed
Mean field Nf value*** 5.46 × 106 4.67 × 106 5.60 × 106
COV of Ln Nf (field)***
------------ ≅ 6.87 - 9.85% ≅ 2.81 – 3.98%
95% field Nf CI *** ≅ 1.93 – 15.34 × 106 ≅ 0.49 – 16.74 × 106 ≅ 2.98 – 8.92 × 106
Note: *Equipment costs were based on July 2004 estimates; **Analysis time estimates based solely on the researchers’ experience with each approach
***Field Nf, COV and 95% CI values based on PS# 1 and WW environment only
An example of the analysis used to obtain the field Nf results shown in Tables 12-1 (c)
and (d) for the ME, CMSE, and CM approaches in PS# 1 and the WW environment is given in
Appendix I. For the M-E Pavement Design Guide, the Nf analysis is software-based. Based on
Tables 12-1 (c) and (d), the field Nf varies across pavement structures, particularly for the ME
and M-E Pavement Design Guide approaches. This variation is attributed to the predominant
sensitivity of these approaches, particularly the ME analysis models, to the critical design tensile
strain, εt,, at the bottom of the HMAC layer, a parameter which is itself largely dependent on the
entire pavement structure. For the ME approach, it should also be noted that the field Nf
predictions strongly depend on the selected shift factor (SF) (Chapter 4).
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Table 12-1(c). Summary Comparison of the Fatigue Analysis Approaches.
Field Nf (WW Environment) PS Mixture ME CMSE CM Design Guide
Bryan 1.03 × 106 3.11 × 106 3.10 × 106 4.71 × 106 1 Yoakum 8.30 × 106 8.40 × 106 7.77 × 106 6.21 × 106 Bryan 0.26 × 106 2.13 × 106 2.38 × 106 4.05 × 106 2 Yoakum 0.97 × 106 6.56 × 106 5.55 × 106 5.75 × 106 Bryan 0.25 × 106 2.18 × 106 2.06 × 106 1.93 × 106 3 Yoakum 0.98 × 106 6.57 × 106 6.23 × 106 3.41 × 106 Bryan 0.28 × 106 1.96 × 106 1.96 × 106 2.02 × 106 4 Yoakum 0.99 × 106 4.45 × 106 4.59 × 106 2.97 × 106 Bryan 2.16 × 106 5.49 × 106 5.38 × 106 19.29 × 106 5 Yoakum ----------- ----------- ------------- -------------
Table 12-1(d). Summary Comparison of the Fatigue Analysis Approaches.
Field Nf (DC Environment) PS Mixture ME CMSE CM Design Guide
Bryan 1.18 × 106 3.60 × 106 3.59 × 106 5.19 × 106 1 Yoakum 9.59 × 106 9.07 × 106 8.46 × 106 8.02 × 106 Bryan 0.34 × 106 2.46 × 106 2.74 × 106 5.23 × 106 2 Yoakum 1.27 × 106 6.78 × 106 5.80 × 106 7.43 × 106 Bryan 0.33 × 106 2.52 × 106 2.39 × 106 4.29 × 106 3 Yoakum 1.27 × 106 6.79 × 106 6.51 × 106 5.57 × 106 Bryan 0.35 × 106 2.26 × 106 2.27 × 106 3.56 × 106 4 Yoakum 1.27 × 106 4.61 × 106 4.79 × 106 5.24 × 106 Bryan 2.18 × 106 6.34 × 106 6.21 × 106 22.00 × 106 5 Yoakum ----------- ----------- ------------- -------------
Theoretical Concepts
Unlike the mechanistic-empirically based M-E Pavement Design Guide and ME
approaches, the CMSE and CM approaches were formulated on the fundamental concepts of
continuum micromechanics and energy theory, with fracture and healing as the two primary
mechanisms controlling HMAC mixture fatigue damage. The CMSE/CM approaches utilize the
fundamental HMAC mixture properties to estimate lab and/or field Nf.
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Input Data
The input data for the CMSE and CM approaches and associated laboratory tests are
comprehensive, which is necessary to sufficiently and adequately predict field Nf by considering
all relevant factors that affect HMAC fatigue performance. The CMSE and CM approaches
incorporate various material properties such as modulus, tensile strength, fracture, healing, and
anisotropy, which is not the case with the ME approach.
The input data for the M-E Pavement Design Guide is also comprehensive but can be
flexible depending on the level of analysis selected. Level 1 requires comprehensive input data in
terms of traffic, environment, and material properties, with HMAC mixture properties
characterized in terms of the |E*| values.
Laboratory Testing
The BB test for the ME approach is comparatively complex and time consuming. Note
also that the laboratory BB equipment is limited to only third-point loading HMAC beam fatigue
testing in a flexural mode. The linear kneading compactor may also be limited to rectangular
beam shaped specimens, while most of the current Superpave HMAC mixture characterization
tests use gyratory compacted cylindrical specimens.
The CMSE laboratory tests may be numerous, but they are relatively simple to run and
less time consuming (provided specimens are well aligned along the axis of loading during
testing). With the exception of SE measurements, the average test time for CMSE testing was at
most 5 hrs. Additionally, CMSE cylindrical specimens are relatively easy to fabricate and
handle. In the case of the CM approach, SE measurements (both for binder and aggregate) and
RM tests in compression are not required, thus making the CM approach even more
advantageous in terms of laboratory testing and subsequent data analysis.
However, with the CMSE uniaxial testing of the HMAC mixtures, it is imperative that
the cylindrical specimens are properly aligned along the axis of loading (tensile or compressive)
to prevent the induction of undesirable moments that can lead to erroneous results.
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DM testing for Level 1 fatigue analysis of the M-E Pavement Design Guide is relative
easy and simple to run but very time consuming in terms of temperature conditioning time for
the specimens. Since a complete DM test for a single cylindrical specimen is often conducted at
five temperatures, the minimum total conditioning time in this project was 10 hrs, i.e., a
minimum of 2 hrs for each test temperature.
BB testing with the ME approach utilizes kneading compacted beam shaped specimens
that are comparatively difficult to fabricate, time consuming to make, and require delicate
handling and storage. Improper handling and/or storage can easily induce residual stresses within
the specimen that can have a negative impact on the results.
Also, the beam shape of the specimens and the linear compaction procedure makes it
difficult to adequately control the AV content to the target level. For instance, the COV of the
AV content for the beam specimens in this project ranged between 4 to 8 percent. While this
COV range may be acceptable, it was nonetheless higher than the approximately 3 to 6 percent
COV for the cylindrical specimens utilized in the M-E Pavement Design Guide and CMSE/CM
approaches. All these factors ultimately contribute to the relatively high variability in both the
input data and final field Nf results for the ME approach.
Failure Criteria
The M-E Pavement Design Guide failure criterion is based on a percentage cracking in
the wheelpath. In this project, the research team used 50 percent as the threshold value consistent
with the TxDOT tolerable limits (61). However, the research team feels that this percent
cracking does not correlate well with the actual fatigue damage accumulation (i.e., crack growth
through the HMAC layer) or crack severity in an in situ HMAC pavement structure. For
instance, a severely cracked HMAC pavement structure with only 10 percent crack area coverage
may be considered adequate according to this criterion. Whereas a 60 percent cracked pavement
section with cracks only initiating (beginning) will be considered inadequate according to this
criterion. Therefore, there may be a need to review this failure criterion.
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In the case of the ME approach, the correlation between fatigue crack area and severity
on an in situ pavement structure and/or crack length through the HMAC layer thickness and 50
percent flexural stiffness reduction is not clear. As pointed out by Ghuzlan et al. (116), 50
percent initial stiffness reduction for constant strain BB testing is an arbitrary failure criterion
that does not correlate well to the actual damage accumulation in the HMAC material. These
researchers instead proposed the use of energy concepts. Rowe et al.’s study also suggests that
while this 50 percent stiffness reduction may work well for unmodified binders, it may not be
applicable for modified binders, and thus, results must be analyzed and interpreted cautiously
(113). Note that the Yoakum mixture with the modified binder generally exhibited higher Ln Nf
(both lab and field) variability in this project.
In addition, the ME assumption of bottom-up crack failure mode due to horizontal εt as
utilized in this project may not always be true particularly for thick, stiff or thin, flexible HMAC
pavement structures. This also applies to the M-E Pavement Design Guide approach. For the
CMSE approach, the failure criterion needs to be further reviewed to establish the adequacy of
assuming one microcrack (7.5 mm) initiating and propagating through the HMAC layer
thickness as representative of the fatigue cracking process in the entire HMAC pavement
structure. The current CMSE version is based on the generalized hypothesis that the growth of
one crack is representative of the field HAMC pavement crack size distribution. Consequently,
more data are thus required to validate this hypothesis.
Both the ME and the M-E Pavement Design Guide utilize tensile strain as the failure
load-response parameter and exhibit considerable sensitivity to this parameter (3, 4, 59). Though
still subject to review, recent research including the preliminary observation of this project has
shown that because of the anisotropic nature of HMAC, this may not always be true, particularly
for thick stiff HMAC pavement structures. Therefore, the use of εt at the bottom of the HMAC
layer may provide an under- or over-estimation of the mixture Nf, particularly for pavement
structures where εt at the bottom of the HMAC layer is not critical to fatigue performance. Based
on this theory, it appears that the ME approach may be applicable only to pavement structures
where εt at the bottom of the HMAC layer is critical to fatigue performance. Otherwise the
approach tended to over predict Nf, particularly for pavement structures with εt less than 100
microstrain in this project. Various researchers, including Nishizwa et al.(34), have also reported
infinite Nf at low strain levels less than 200 microstrain with the ME approach.
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Data Analysis
In terms of analysis, the CMSE and CM approaches are comparatively complex and
lengthy because of the comprehensive input data requirements. Inevitably, this type of analysis is
necessary to adequately model the HMAC mixture fatigue resistance by analyzing and directly
incorporating all the influencing factors. However, these numerical calculations can easily be
simplified if a simple spreadsheet analysis program is developed for the computations, as was the
case in this project. Alternatively, a CMSE/CM fatigue analysis software can be developed to
simplify and reduce the time needed for these calculations.
Nonetheless, a comprehensive sensitivity analysis of the CMSE/CM fatigue analysis
procedure is recommended to simplify the calculations by eliminating/reducing less critical
and/or redundant variables. While the CMSE/CM analysis procedure produced reasonable results
in this project, it should be noted that this is a relatively new fatigue analysis procedure and may
therefore still be subject to review and modifications in continuing research work during the
validation phase.
For the ME approach, the simplified AASHTO TP8-94 analysis procedure utilized in this
project was relatively easy and straightforward, probably because of the relatively fewer input
data required (59). For the M-E Pavement Design Guide, the fatigue analysis process is software
based but utilizes the ME concepts (3, 4).
While the ME laboratory-to-field shift factors (SF) may be environmentally specific and
require calibration to local conditions, the CMSE/CM calibration constants were developed
based on a wider environmental spectrum covering the USA (45), thus making the CMSE
approach more flexible. By contrast, the M-E Pavement Design Guide incorporates a
comprehensive climatic model that computes the shift factors based on a specific environmental
location (3, 4). The M-E Pavement Design Guide Level 1 fatigue analysis actually computes
these calibration constants based on actual climatic (current or past) data from local weather
stations. In this context, the M-E Pavement Design Guide may therefore be considered as being
more accurate and realistic in terms of simulating field environmental conditions compared to
the other fatigue analysis approaches. The M-E Pavement Design Guide software also
encompasses a comprehensive traffic analysis model that more closely simulates field traffic
loading conditions than the ME and CMSE/CM approaches (3, 4).
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Furthermore, the M-E Pavement Design Guide software incorporates a default
empirically-based Global Aging Model that takes into account the effects of aging in HMAC
mixture fatigue analysis (3, 4). By contrast, the ME and the current CMSE/CM approaches do
not directly incorporate the effects of aging in the analysis. In the case of the CMSE approach,
attempts are being made to develop shift factors due to aging (Chapters 10 and 11) in the
ongoing research and will possibly be incorporated in the final CMSE version. For the ME
approach, Miner’s hypothesis (18) can be utilized to develop and incorporate the effects of aging
in field Nf prediction, but this was beyond the scope of this study.
Additionally, the M-E Pavement Design Guide software has an added advantage of
simultaneously predicting other HMAC pavement distresses besides fatigue cracking. These
include thermal cracking, rutting, and pavement roughness expressed in terms of the
international roughness index (IRI). The CMSE approach on the other hand, has the potential to
simultaneously model HMAC moisture sensitivity through the use of surface energy data under
wet conditions (46, 47, 68, 71). In this project, however, dry conditions were assumed with no
consideration of moisture sensitivity analysis for the HMAC mixtures.
Results and Variability
Although the computed mixture field Nf results presented in Chapters 10 and 11 were
comparable, the CMSE and CM approaches exhibited relatively low variability in terms of the
COV of Ln Nf compared to both the ME and the M-E Pavement Design Guide approaches. As
highlighted in Chapter 11 (Table 11-2), the ME approach exhibited the highest statistical
variability both in terms of the COV of Ln Nf and 95 percent field Nf CI. Furthermore, the ME
field Nf predictions are significantly dependent on the selected SF value (Chapter 4), which will
obviously lead to different results if a different SF value is selected. Note that this SF value for
the ME approach was not measured in this project (Chapter 4).
Although this lower statistical variability may also indicate that the CMSE/CM test
repeatability was better than the BB and DM tests, more comprehensive statistical analyses for
the CMSE/CM approaches are required, including more laboratory HMAC mixture fatigue
characterization and field validation.
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Costs – Time Requirements for Laboratory Testing and Data Analysis
The cost comparisons in this project were evaluated in terms of billable time
requirements for laboratory testing (specimen fabrication, machine set up, and actual test running
time) and data analysis. These typical time estimates based on at least four HMAC specimens for
the ME and CMSE/CM approaches and at least two HMAC specimens for the M-E Pavement
Design Guide to obtain at least a single value of field Nf are shown in Table 12-1.
Detailed time requirements are attached as Appendix J. Note that these time estimates
were purely based on the work contained in this project, but actual time requirements for
laboratory testing and data analysis may generally vary from one person to another and from
machine to machine or computer to computer (e.g., in the case of the M-E Pavement Design
Guide).
In Table 12-1, laboratory testing time does not include aggregate pre-heating, binder
liquefying, short-term oven aging, heating for compaction, cooling after compaction, and
temperature conditioning time of the specimens prior to testing, because time for these processes
was considered equal in each approach and may often not be billable. Based on the billable time
requirements in Table 12-1, the M-E Pavement Design Guide was ranked as the cheapest
(shortest billable time requirement) followed by the CM approach.
Generally, the ME approach required more time for specimen fabrication, machine setup,
and actual testing but less time for data analysis primarily due to the simplified AASHTO
TP8-94 analysis procedure selected and the fewer input data requirements (59).
For the CMSE approach, SE values for binders and aggregates are required as input data.
Though the current test protocol for aggregates might require a test time of about 30 to 60 hrs per
aggregate, various alternate and time-efficient SE measurement methods are being investigated
in an ongoing research project (77). Despite the lengthy test time, however, SE measurements
are only performed once for any binder or aggregate type from a particular source (as long as
there are no major compositional changes). The SE data can then be utilized for numerous
analysis applications including fatigue, permanent deformation, and moisture sensitivity
modeling in HMAC pavements. Thus, SE measurements are actually efficient considering their
repeated and widespread use for binder and aggregate materials that may be utilized in different
mixture designs for different projects.
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Costs – Equipment
In terms of equipment cost, the CMSE was ranked as the most expensive approach with
an approximate total cost of $210,000 (with about $80,000 being for the SE equipment) followed
by the ME approach, based on current equipment costs. Although the SE equipment appears
costly, its versatility in terms of data measurements for HMAC mixture fatigue, permanent
deformation, and moisture sensitivity analysis may actually offset the high initial cost. This is
especially significant for numerous concurrent projects.
The equipment costs for the M-E Pavement Design Guide (≅ $130,000) and the CM (≅
$210,000 - $80,000 = $130,000) approaches are similar. However, the cost of the M-E Pavement
Design Guide software, which is not included in Table 12-1, may raise the M-E Pavement
Design Guide total cost to a value higher than that of the CM approach.
The ME equipment cost is lower than that of the CMSE, but it exceeds the M-E
Pavement Design Guide and the CM approaches by approximately $25,560 based on the current
price of the BB device (Table 12-1) (118). The limited use of the BB device for flexural fatigue
testing only also indirectly makes the ME approach more costly.
SELECTION OF FATIGUE ANALYSIS APPROACH
Table 12-2 summarizes the advantages and disadvantages of each fatigue analysis
approach as observed in this project. Table 12-3 is a summary rating based on a comprehensive
value engineering assessment including laboratory test results, statistical analysis, and relative
comparison of each analysis procedure. The assessment and rating criteria, including a TxDOT
evaluation survey questionnaire to rate the assessment factors according to their degree of
significance, are discussed in this section. A detailed rating analysis is attached as Appendix K.
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Table 12-2. Summary Comparison of the Fatigue Analysis Approaches.
Approach Advantage Disadvantage
CMSE • Utilizes fundamental HMAC mixture properties to estimate Nf • Exhibits greater flexibility & potential to incorporate material properties that are
critical to HMAC mixture fatigue performance • Utilizes shear strain as failure load-response parameter • Utilizes cylindrical specimens that are easy to fabricate & handle • Requires numerous tests that are easy & relatively less costly to run • Relates fatigue failure to damage accumulation within HMAC material • Procedures Nf results that exhibits lower statistical variability • Produces fatigue performance results as a function of microcrack growth through
HMAC layer thickness • Utilizes calibration constants that were developed nationwide • Incorporates aging, healing, & anisotropic effects in Nf analysis • Laboratory tests and resultant data are versatile in their application
• Validity & applicability • More mixture characterization • Test protocols & analysis procedure subject to
review • Lab testing – specimen alignment • Adequacy of failure criteria • Statistical analysis criteria needs more review • SE testing is lengthy & costly
CM • Same as CMSE but with no SE tests & reduced analysis
M-E Pavement Design Guide
• Ideal for pavement structures where tensile strain is critical to fatigue performance
• Incorporates global aging model • Predicts distress as a function of pavement age • Incorporates comprehensive traffic and climatic analysis models • Utilizes cylindrical specimens that are easy to fabricate & handle • Tests are easy and less costly • Failure criteria is based 50 % cracking in wheelpath • Versatility – other tests & analyses
• Empirically based • Global aging model may not be good for
modified binders • No direct incorporation of healing nor
anisotropy • Failure criteria does not clearly relate to
damage & severity • Only bottom-up cracking failure mode was
considered in this study. ME • Ideal for pavement structures where tensile strain is critical to fatigue
performance • Requires local calibration to field conditions • Failure criteria is based on 50% stiffness reduction
• Empirically based • Beam specimen are difficult to fabricate and
handle • Laboratory testing is lengthy • No direct incorporation of aging, anisotropy, &
healing effects in analysis • High variability in results • Not applicable to pavement structures where
tensile strain critical to fatigue performance • Test equipment is limited to BB testing only.
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TxDOT Evaluation Survey Questionnaire
An evaluation survey questionnaire was conducted with TxDOT personnel to ascertain
the degree of significance of the various factors to be used in evaluating and rating the four
fatigue analysis approaches consistent with the TxDOT HMAC mixture fatigue characterization
and pavement structural design for fatigue resistance. These factors include laboratory testing,
material properties, input data variability, analysis, field Nf results, and associated costs.
Appendix K is an example of the evaluation survey questionnaire and shows the sub-factors
associated with each factor. For each factor and sub-factor, the rating score was from 1 to 10,
with 10 representing the most significant factor/sub-factor and 1 being the least significant.
Figure 12-1 summarizes these rating results in a decreasing order of significance for both
the factors and sub-factors. Based on these rating scores, the averaged weighting scores out of a
total score of 100 percent were determined and are shown in parentheses in Figure 12-1.
According to these rating results, mixture field Nf results in terms of variability and tie to field
performance is the most significant factor to consider when selecting and recommending an
appropriate fatigue analysis approach to TxDOT. This factor has a weighting score of 22 percent.
Material properties were considered the least significant factor with a total weighting score of 14
percent. Within the factor “material properties,” mixture volumetrics (binder content and AV)
and modulus/stiffness were considered the most significant sub-factors with an equal weighting
score of 17 percent, while anisotropy was the least significant (9 percent). It is also worthwhile to
note that the factors “analysis” and “laboratory testing” have the same degree of importance
(with an equal weighting score of 15 percent).
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Results (22%)
Nf variability (50%) Tie to field performance (50%)
Costs (18%) Practicality of implementation (32%) Laboratory testing (hrs) (32%) Analysis (hrs) (19%) Equipment ($) (17%)
Input data (16%) Materials (36%) Traffic (34%) Environment (30%) Analysis (15%) Failure criteria (41%) Simplicity (36%) Versatility of inputs (23%) Laboratory testing (15%) Simplicity (32%) Equipment availability (29%) Equipment versatility (22%) Human resources (18%)
Material properties (14%) Mixture volumetrics (17%)
Modulus/stiffness (17%) Fracture (16%) Tensile strength (15%) Aging (14%) Healing (12%) Anisotropy (9%)
Figure 12-1. Assessment Factors/Sub-factors and Associated Weighting Scores.
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Assessment and Rating Criteria of the Fatigue Analysis Approaches
Using Tables 12-1 and 12-2, the research team assigned scores (out of 10) to each
sub-factor, as shown in Appendix L. For this analysis, the scores (with a range of 0 to 10) for
each sub-factor, e.g., those associated with the factor “results,” were defined as follows:
• Variability: 10/10 ≅ low, 5/10 ≅ low to high, and
0/10 ≅ high variability.
• Tie to field performance: 10/10 ≅ high, 5/10 ≅ low to high, and
0/10 ≅ low degree of or poor tie to field performance.
Using Figure 12-1, the weighted scores for each factor for each approach were summed
up as shown in Appendix L. Table 12-3 provides an evaluation summary of the scores and
ratings of the fatigue analysis approaches.
Table 12-3. Weighted Scores and Rating of the Fatigue Analysis Approaches.
Evaluation Score Category Weight
Guide ME CMSE CM
Results 22% 11% 9% 14% 13%
Cost 18% 12% 10% 12% 13%
Input data variability 16% 12% 8% 10% 10%
Analysis 15% 9% 9% 11% 10%
Laboratory testing 15% 12% 6% 12% 12%
Incorporation of material properties
14% 10% 8% 13% 12%
Total 100% 66% 50% 72% 70%
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Table 12-3 shows the weighting scores associated with each factor and the actual score
assigned for each approach. “Results,” for instance, has a total weighted score of 22 percent. For
this factor, the CMSE approach scored the highest score (14 percent) and would be ranked first
based on this factor. In terms of laboratory testing, while all the other approaches have the same
ranking based on equal scores (12 percent), the ME approach would be ranked last with a score
of 6 percent out of a weighted total of 15 percent. In terms of the overall scores (out of a total of
100 percent), the order of ranking is CMSE (72 percent), CM (70 percent), M-E Pavement
Design Guide (66 percent), and ME (50 percent).
The Selected Fatigue Analysis Approach – The CMSE Approach
Based on this value engineering assessment, as shown in Table 12-3, and considering the
test conditions in this project, the CMSE fatigue analysis approach with the highest score (75
percent) is recommended for predicting HMAC mixture fatigue life. With the possibility of
establishing a SE database in the future from various ongoing TxDOT projects, the CMSE
approach will become a reality both in terms of further validation and practical implementation.
Furthermore, a sensitivity analysis with more HMAC mixture characterization to streamline the
CMSE procedure will make the approach simple and practical to implement.
Based on the score ranking, the CM is recommended as the second alternative approach
in lieu of the CMSE approach to be utilized particularly in the absence of SE data. Note,
however, that the CM analysis models were modified in this project based on the CMSE results.
Consequently, more independent HMAC mixtures need to be characterized for fatigue resistance
to validate this correlation between the CMSE and the CM approaches. With further validation
through additional HMAC mixture characterization, CM is a potentially promising fatigue
analysis approach to be recommended over CMSE possibly at the end of this project.
Although the CMSE fatigue analysis approach is recommended in this project, it should
be noted that any fatigue design approach can produce desired results provided it is well
calibrated to the environmental and traffic loading conditions of interest and that all relevant
factors affecting performance are appropriately taken into consideration.
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Incorporation of Aging Effects in Field Nf Prediction
With further research and more binder and HMAC mixture fatigue characterization, a
shift factor due to aging (SFag or SFaging) will possibly be incorporated in the CMSE fatigue
analysis model, as illustrated in Chapters 10 and 11. While some aging shift factors were
developed in this project (SFag in Chapter 10 and SFaging in Chapter 11), validation of these
concepts is still required through testing of additional binders and HMAC mixtures. In contrast
to the simplicity adopted in these concepts, HMAC aging should possibly be modeled as a
function of three processes: binder oxidation, binder hardening, and field Nf reduction.
Additionally, the SFag (or SFaging) should be able to account for mix-design
characteristics, traffic loading, and environmental conditions. As pointed out in Chapter 10, field
HMAC aging is a relatively complex process involving fluctuating traffic loading and
environmental conditions. Note, however, that traffic (in terms of design ESALs) and
environmental effects (in terms of temperature) are also taken into account by the SFh (Chapter
5) in this CMSE approach. In addition, the rate of aging or response to binder oxidation and
hardening and subsequent reduction in fatigue resistance may differ from mixture to mixture
depending on the material type and mix-design characteristics. Most importantly, the SFag (or
SFaging) must be derived as a function of time so that Nf at any pavement age can be predicted.
Once these SFag have been developed and validated for a group of similar HMAC mixtures,
laboratory testing of aged HMAC mixtures may be unnecessary.
Recommendations on a Surrogate Fatigue Test and Analysis Protocol
The fatigue analysis approaches discussed in this report and the selected CMSE approach
incorporate stress-strain analysis that depends on both pavement structure and environmental
location. This is because stress and/or strain are required as an input parameter in these analyses.
Unlike other distresses, such as rutting or permanent deformation, fatigue cracking in the HMAC
layer depends on the entire pavement structure and its response to both traffic loading and the
environment. Consequently, a surrogate fatigue test and analysis protocol that is independent of
the pavement structure and environment cannot be recommended based on the fatigue analysis
approaches and results presented in this report. However, investigation of surrogate fatigue test
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protocols based on CMSE testing for use in mix design and HMAC mixture screening without
prediction of Nf is reported in Research Report 0-4468-3.
In the absence of a fatigue analysis model that is independent of stress and/or strain as
input parameters, the research team proposes establishing a database of a range of design stress
and/or strain levels for typical TxDOT HMAC pavement structures and the Texas environment.
Establishment of such a database to be used in conjunction with these fatigue analysis
approaches will facilitate an easier and quicker way of characterizing the fatigue resistance of
HMAC mixtures using some of the tests described in this report as surrogate tests. This will also
eliminate the need to conduct an extensive stress-strain analysis every time a HMAC mixture is
to be characterized for fatigue resistance.
SUMMARY
Key points from a comparison and selection of the fatigue analysis approaches are
summarized as follows:
• The four fatigue analysis approaches (ME, CMSE, CM, and M-E Pavement Design Guide)
were comparatively analyzed in terms of the following factors: theoretical concepts, input
data, laboratory testing, failure criteria, data analysis, results and variability, and associated
costs.
• Selection of the fatigue analysis approach was based on field Nf results, costs, input data
variability, analysis, laboratory testing, and incorporation of material properties consistent
with the TxDOT level of significance of each parameter. Based on this value engineering
assessment criteria and considering the test conditions in this project, the CMSE fatigue
analysis approach was selected and recommended for predicting HMAC mixture field Nf.
• Although the CMSE fatigue analysis approach was selected in this project, any fatigue
analysis approach can produce desired results provided it is well calibrated to the
environmental and traffic loading conditions of interest and that all relevant factors affecting
fatigue performance are appropriately taken into account.
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CHAPTER 13 CONCLUSIONS, RECOMMENDATIONS,
AND FUTURE WORK
From the data presented and analyzed in this interim report, the following conclusions,
recommendations, and future work plans are presented.
CONCLUSIONS
The selected fatigue analysis approach, a comparison of mixture field Nf, the effects of
binder oxidative aging and other input variables, binder and binder-mixture results are
summarized in this section.
Selected Fatigue Analysis Approach – CMSE
(1) Based on a value engineering assessment including laboratory testing, input data, statistical
analysis, costs, and the analysis procedure of each approach, the CMSE fatigue analysis
approach is recommended for predicting HMAC mixture fatigue life.
(2) In comparison to other approaches that were evaluated and for the test conditions considered
in this project, the CMSE approach exhibited better mixture field Nf prediction capability:
• It utilizes fundamental mixture properties to estimate field Nf, and incorporates the
continuum micromechanics-energy theories of fracture and healing in the fatigue analysis
of HMAC mixtures.
• It exhibits greater flexibility and the potential to account for most of the fundamental
HMAC material properties that affect HMAC pavement fatigue performance. These
properties include fracture, binder aging effects, healing, visco-elasticity, anisotropy,
crack initiation, and crack propagation.
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• With the exception of SE measurements, the CMSE laboratory tests are less costly both
in terms of billable time requirements and equipment. Laboratory testing for this
approach utilizes gyratory compacted specimens that are relatively easy to fabricate and
handle compared to beam specimens for the ME approach.
• The failure criterion of a 7.5 mm (0.3 inches) microcrack initiation, growth, and
propagation through the HMAC layer thickness closely correlates with actual fracture
damage accumulation in an in situ HMAC pavement structure compared to the failure
criteria of the other approaches, the M-E Pavement Design Guide and the ME approach.
• The CMSE mixture results exhibited lower variability in terms of the COV of Ln Nf.
• Has the potential to simultaneously model HMAC moisture sensitivity through the use of
surface energy data under wet conditions.
(3) Although the SE measurements for the CMSE analysis are lengthy in terms of test time, the
tests are performed only once for any binder or aggregate type from a particular source (as
long as there are no major compositional changes). The SE data can then be utilized for
numerous analysis applications including fatigue, permanent deformation, and moisture
sensitivity modeling in HMAC pavements. Thus, SE measurements are actually efficient
considering their repeated and widespread use for binder and aggregate materials that may be
utilized in different mixture designs in different projects.
(4) In the absence of SE data, the CM approach can be utilized in lieu of the CMSE approach.
The fundamental concepts, failure criteria, and analysis procedure are basically similar,
except for the following:
• SE laboratory measurements (both for binders and aggregates) and RM tests in
compression are not required in the CM approach.
• SE input data for both the binder and aggregate are not required in the CM approach.
Instead, the CM approach utilizes empirical relationships that were calibrated to the
CMSE approach to compute SFh and Paris’ Law fracture coefficients that are dependent
on RM (compression) and SE data in the CMSE approach.
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Comparison of Mixture Field Nf
(1) The Yoakum mixture exhibited better fatigue resistance in terms of the field Nf values for all
aging and environmental conditions and for all pavement structures considered in this project
compared to the Bryan mixture. This finding was observed in all the fatigue analysis
approaches. Also, the Yoakum mixture exhibited less susceptibility to aging compared to the
Bryan mixture. The research team hypothesizes that the Yoakum mixture’s improved fatigue
performance may be due to the following factors:
• The higher binder content for the Yoakum mixture (5.6 percent by weight of aggregate)
probably increased its fatigue resistance compared to the Bryan mixture, which was a 4.6
percent binder content by weight of aggregate.
• The effect of the SBS modifier and the 1 percent hydrated lime in the mixture could have
possibly decreased the Yoakum mixture’s susceptibility to oxidative hardening. In their
study, Wisneski et al. made similar observations that hydrated lime tended to improve the
performance of recycled asphalt (114). However, this phenomenon is yet to be explored
in greater depth.
• The binder-aggregate bond strength, as exhibited by the SE results, indicated a relatively
better bond compatibility for the Yoakum mixture (PG 76-22 plus gravel aggregate) than
for the Bryan mixture (PG 64-22 plus limestone aggregate).
(2) For the field Nf results, the Yoakum mixture exhibited higher variability in terms of the COV
of Ln Nf and 95 percent CI range.
Effects of Binder Oxidative Aging and Other Variables
(1) Binder aging reduces HMAC mixture resistance to fracture and ability to heal. Generally, all
mixtures exhibited a declining field Nf with aging.
(2) Both binders and mixtures stiffen with aging, and these changes quantitatively correlated
with each other.
(3) HMAC mixture field Nf performance depends on both pavement structure and environmental
conditions.
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(4) The computed temperature shift factors (aT) for the HMAC mixtures based on
time-temperature superposition principles using the Arrhenius model exhibited a linear
relationship with temperature. While these aT showed some sensitivity to mixture type, they
were by and large insensitive to binder oxidative aging effects.
Binder-Mixture Characterization
(1) Mixtures stiffen significantly in response to binder oxidative aging.
(2) For a given mixture specimen, mixture stiffening correlates directly to binder stiffening.
(3) The change in mixture stiffness for different mixtures relates differently to binder stiffness.
The Bryan mixture has a softer binder but a stiffer mixture compared to the Yoakum mixture.
(4) Mixture fatigue life declines significantly when the binder stiffens due to oxidative aging.
The amount of decline for a given amount of binder stiffening can vary significantly from
one mixture to the next.
(5) The decline in fatigue life with binder hardening appears to have a dramatic effect on
pavement service life. Thus, differences between mixtures and the impact of binder aging
on fatigue life can have a very significant impact on pavement life-cycle cost.
(6) From the binder-mixture relationships, aging shift factors (SFag) based on the binder
visco-elastic properties were developed for each mixture type, and a relationship was
developed between binder properties and mixture field Nf values. With more HMAC fatigue
characterization, development of a single set of SFag coefficients for a different group of
similar mixtures will inevitably allow for prediction of Nf at any pavement age without the
need to test aged mixtures.
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RECOMMENDATIONS
From the findings of this project, the following recommendations were made.
(1) More HMAC mixture laboratory fatigue characterization is recommended to:
• provide confidence and validation in the selected CMSE approach. The CMSE laboratory
test protocol, failure criteria, and analysis procedure should be reviewed and if needed,
modified accordingly. For instance, the 7.5 mm (0.3 inches) microcrack threshold should
be reviewed to establish its adequacy as representative of the fatigue cracking process in
the entire HMAC pavement structure. The current CMSE version is based on the
generalized hypothesis that the growth of one crack is representative of the field
pavement crack size distribution.
• populate the field Nf database of commonly used TxDOT rut resistant mixtures.
• provide additional data so as to adequately model and incorporate the effects of binder
oxidative aging.
(2) A numerical analysis software for the CMSE (and CM) fatigue analysis approach(es) should
be developed based on the analysis procedure described in this report. Such a program will
among others lead to the following benefits:
• simplify and reduce the time required for the CMSE/CM fatigue analysis process.
• minimize human associated errors resulting from manual calculations.
• facilitate a faster methodology of conducting a sensitivity analysis on the CMSE/CM
approach so as to reduce/eliminate redundant variables in CMSE/CM analysis models.
• facilitate a quicker and convenient way to validate and, if need be, modify the CMSE/CM
approach based on more laboratory HMAC mixture characterization.
(3) Because of the apparent importance of fatigue decline with oxidative binder stiffening, more
work is needed to understand this phenomenon and the essential features of mixture design
that impact this decline. This effect is believed to be as much a mixture as a binder property
and, if so, can only be established and understood through additional, carefully designed
combined mixture-binder studies.
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(4) For CMSE uniaxial laboratory testing, it is strongly recommended that the specimens must
always be properly aligned along the central axis of loading to minimize the induction of
undesirable moments that can lead to erroneous results.
CLOSURE
The CMSE/CM approaches described in this interim report are relatively new analysis
procedures for fatigue characterization of HMAC mixtures and therefore still may be subject to
review and/or modifications. These approaches predict Nf and recognize the dependence of
fatigue cracking on the entire pavement structure when subjected to traffic loading. Investigation
of surrogate fatigue test protocols based on CMSE testing for use in mix design and HMAC
mixture screening is reported in Research Report 0-4468-3.
CURRENT AND FUTURE FY05 WORK
In the modified project, the research team plans to expand on the materials characterized
in this interim report. This laboratory characterization of more HMAC mixtures will increase the
TxDOT field Nf database, validate and provide more confidence in the selected CMSE/CM
approach and, if need be, provide guidance on any necessary modifications. The third year will
also provide more data for understanding the important phenomenon of binder oxidative aging
and its influence on HMAC mixture fatigue resistance as well as developing shift factors to
account for binder oxidative aging when estimating mixture field Nf.
Based on the limited timeframe and budget for the third year, mixture design for the
FY05 mixtures will be limited to Superpave mixes only, with gravel as the only aggregate to be
used. PG 64-22 and PG 76-22 binders will be used with two modifiers (SBS and tire rubber
(TR)). In line with the prime objective and title of the overall project, the emphasis of the third
year work plan is to characterize more rut resistant mixtures and compare the subsequent
findings to the Yoakum mixture as well as to further investigate the effect of binder oxidative
aging on the mixture fatigue resistance. Consequently, the focus of the modified project will be
on modified binders, which provide rut resistant mixtures.
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Two binder content levels, optimum and optimum plus 0.5 percent, consistent with
TxDOT recommendations, will be utilized to investigate the effect of binder content on the
fatigue resistance of the rut resistant mixtures. In terms of aging conditions, only two (0 and 6
months at 60 °C [140 °F]) will be addressed to supplement the 0, 3, and 6 months aging
conditions.
Table 13-1 summarizes the possible FY05 mixtures based on a comprehensive factorial
experimental design that can estimate all the main factors (binder type-modifier type (BTMT),
binder content (BC), and aging) considered in the third year and the two-way interactions
(BC*aging, BTMT*aging, and BTMT*BC).
Table 13-1. Example of a Factorial Experimental Design for FY05.
Run/Mixture Binder Type-Modifier Type
Binder Content Aging Condition (Months)
1 PG 76-22_SBS Optimum 02 PG 76-22_TR Optimum 0
3 PG 76-22_SBS Optimum + 0.5% 04 PG 76-22_TR Optimum + 0.5% 05 PG 64-22 Optimum 06 PG 64-22 Optimum + 0.5% 0
7 PG 76-22_SBS Optimum 6
8 PG 76-22_TR Optimum 6
9 PG 76-22_SBS Optimum + 0.5% 6
10 PG 64-22 Optimum 611 PG 64-22 Optimum + 0.5% 6
12 PG 76-22_TR Optimum + 0.5% 6
Note that the mixtures in Italics (Runs # 1 and 7) in Table 13-1 are the rut resistant
mixtures already characterized in Phase I and presented in this interim report. At the end of the
project in the third year modification, the following will be addressed:
• validation and provision of more confidence in the selected and recommended CMSE
approach through utilization of more HMAC mixtures,
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246
• a database of mixture field Nf results based on the CMSE approach,
• a better understanding and quantification of the binder-mixture relationships and effects of
binder oxidative aging,
• development of a shift factor due to aging to be incorporated in the CMSE approach,
• investigation of the effects of binder content and modification on mixture field Nf and aging,
• development of a fatigue design check criteria for the CMSE fatigue analysis approach, and
• investigation of the possibility of establishing a surrogate fatigue test protocol based on
CMSE testing (TS, RM, or RDT) for use only in mix design and HMAC mixture screening
without prediction of Nf
Page 267
247
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APPENDIX A: EVALUATION FIELD SURVEY QUESTIONAIRE (FOR GOVERNMENT AGENCIES AND THE INDUSTRY)
TxDOT PROJECT 0-4468 FATIGUE RESISTANT MIXES AND DESIGN METHODOLOGY SURVEY
This survey is conducted as part of the Texas Department of Transportation (TxDOT) research Project No. 0-4468, Evaluation of the
Fatigue Resistance of Rut Resistant Mixes, under the supervision of Gregory Cleveland (512-506-5830). The primary goal of this project is to
develop and recommend the process for incorporating fatigue analysis and testing into TxDOT's pavement design and mixture design process.
TxDOT already has the means to screen out mixtures that are susceptible to rutting; mixtures with stiffer binders greatly decrease the risk of
premature failure due to rutting. However, there are concerns that some of the mixtures that are highly resistant to rutting may be more prone to
fatigue failure. To identify, document, and compare several materials, mixtures, and pavement structure types in terms of fatigue resistance, we
are sending out this survey to several government agencies and industry representatives in order to create a complete knowledge database.
We would appreciate your participation. If there are any questions concerning this survey or this project, please contact Dr. Amy Epps
Martin (979-862-1750) of the Texas Transportation Institute. Once again we appreciate your time and assistance.
Agency Name: __________________________________ Contact Name: ____________________________________
Phone: ( ____ ___ ) - ____________ - __________ Fax: ( ________ ) - ____________ - __________
_____________________________________________________________________________________________________________________
1. Do you utilize any methodology or approach to design and/or check for fatigue resistance?
YES __________ please proceed to question 2. NO __________ please stop.
2. What mix design methodology(ies) or approach(es) do you follow? _____________________________________________
3. List literature references you have found useful to approach fatigue resistance designs.
____________________________________________________________________________________________________________
4. List the laboratory tests, and corresponding standards, performed as part of the fatigue resistance approach(es) you use.
____________________________________________________________________________________________________________
5. What type(s) of aggregate(s) and binder(s) grades do 6. What pavement structure(s) do you commonly use for you use for fatigue resistant mixes? fatigue resistant pavement design?
Aggregate Type Binder Grade
Layer Thickness Elastic
Modulus
7. What type and amount of resources (time, persons, equipment, etc.) do you require to perform a fatigue resistant mix and pavement design?
Thank you for your time and effort in completing this survey. The results will aid us to identify, document, and compare several materials, mixtures, and pavement structure types in terms of fatigue resistance.
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APPENDIX A (CONTINUED): SUMMARY RESULTS OF EVALUATION FIELD SURVEY
QUESTIONAIRE
(FROM GOVERNMENT AGENCIES AND THE INDUSTRY)
TxDOT PROJECT 0-4468: FATIGUE RESISTANT MIXES AND DESIGN METHODOLOGY SURVEY
Table A1. Summary of Respondent Questionnaire Survey Details.
Materials Pavement Structures No. Agency Contact Fatigue
Methodology Laboratory
Tests Aggregate Binder Layer Thickness Modulus Resources Standards/
References
1
Advanced Asphalt Technologies, LLC
D W. Christensen 814-278 1991
Continuum damage analysis (NCHRP 9-25 and 9-31)
Uniaxial fatigue testing
9.5 – 12 mm, dense gradation
- - - -
-16 hrs -Compactor, ovens, molds, saw, coring rig, MTS system
AAPT papers on Continuum Damage modeling & analysis
2 Abatech G.Rowe 215 – 215 258
Superpave Bending beam and SHRP IDT - - - - - ≥ $40,000 Various paper
publications
3 Louisiana DOTD
C.Abadie 225-767 9109
Superpave
Modified T-283, Moisture sensitivity & retained ITS
Various PG 76-22 Modified - -
Use SN criteria, i.e. 0.44 to 0.48 for HMAC
No special design procedure for fatigue
Superpave
4 North Carolina State University
Y.R. Kim 619-515 7758
Visco-elastic continuum damage model
Uniaxial tension & indirect tension
Granite PG 64-22 - - - MTS & graduate students
-
5 Minnesota DOT
S. Dai 651-779 5218
Superpave & MnPave
No fatigue tests - - Mechanistic-empirically based One
researcher Superpave
6 UCB, Berkeley
M.O. Bejarano 510-231-5746
Caltrans & Asphalt Institute
Bending beam, AASHTO TP-8
Crushed stone, dense graded
AR 4000 AR 8000 AC 150 mm 1000 to
8 000 MPa
-2-3 wks -4 people -bending beam device (Cox & Sons)
-NCHRP 39 -Various publications
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APPENDIX B : HMAC ANISOTROPIC ADJUSTMENT FACTORS
Table B1. Example of Determination of Anisotropic Adjustment Factors (ai). HMAC Elastic Modulus
(MPa) Under Unconfined Conditions
HAMC Elastic Modulus (MPa) Under Confined
Conditions
Test#
Ex(u) Ez(u) Ex(c) Ez(c)
ax = Ex(c)/Ex(u)
az =
1/(Ez(c)/Ex(u))
1 1789 3399 1940 4450 1.08 0.76
2 1569 2980 1785 3927 1.14 0.76
3 1678 3188 1963 4320 1.17 0.74
4 1589 3219 1900 4180 1.20 0.77
5 1498 2846 1760 3972 1.17 0.71
Mean 1625 3127 1870 4170 1.15 0.75
Stdev 112 216 92 223 0.04 0.02
COV 6.90% 6.91% 4.91% 5.35% 3.76% 2.96%
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APPENDIX B (CONTINUED):
THE UNIVERSAL SORPTION DEVICE
Table B2. Summary of the Testing and Analysis Procedure for Determining the Surface Energy of Aggregates Using the USD Method.
Step Action
1 The aggregate sample is prepared from the fraction passing the No.4 (4.75mm) sieve, retained on
the No.8 (2.36mm) sieve.
• Wet sieve approximately 150 g of each type of aggregate. • Wash the samples again using distilled water and dry in a 120 °C (248 °F) oven for at least
8 hrs. • Move the samples into a vacuum desiccator at about 1 torr and 120 °C (248 °F) for at least
24 hrs to de-gas. • Wash the aggregate sample holder with distilled water and acetone and then dry in a 120°C
(248 °F) oven for 1 hr. 2 Place the weighed aggregate in the container and proceed with chamber conditioning:
• Connect the temperature control circulator with the high-pressure steel chamber. • Activate and calibrate the Magnetic Suspension Balance. • Use the vacuum pump to evacuate the chamber to below 1 torr for one day while it is
heated up to 60 °C (140 °F). • Reduce and maintain the chamber temperature at 25°C (77 °F) under the vacuum of below
1 torr for 8 hrs. 3 Proceed with testing using the selected solvents: n-hexane (apolar), methyl-propyl-ketone (mono-
polar) and water (bipolar):
• Initiate the computer program to control testing and control data capturing and enter 8 to 10 predetermined pressure steps based on the saturation vapor pressure of the solvents used. The following two steps are then controlled automatically and is included for completeness of process description.
• Solvent vapor is injected into the system until the first predetermined value is reached by using the macro-adjustment valve. After the steady-state adsorption mass is reached and measured by the system, the pressure is changed to the next setting point.
• Last step is repeated while the computer records the absorbed mass and vapor pressure until the saturated vapor pressure of solvent is reached.
4 Use the specific amount of solvent adsorbed on the surface of the adsorbent and vapor pressure at
the surface of the asphalt or aggregate to do surface energy calculations:
• Calculate the specific surface area of the aggregate using the BET equation. • Calculate the spreading pressure at saturation vapor pressure for each solvent using Gibbs
adsorption equation. • Calculate the three unknown components of surface energy utilizing the equilibrium
spreading pressure of adsorbed vapor on the solid surface and known surface energies of the a polar, mono-polar, and bipolar solvents.
5 Using SE results from step 4, calculate the total surface energy of the aggregate.
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APPENDIX C: BENDING BEAM LABORATORY TEST DATA FOR THE MECHANISTIC EMPIRICAL APPROACH
Table C1. ME Mixture N Data for 0, 3, and 6 Months Aging Conditions. Rows Micro
Strain Nf LabBryan-
0M
Nf Lab Bryan-
3M
Nf Lab Yoakum-
0M
Nf Lab Yoakum-
3M
Nf Lab Yoakum-
6M 1 374 131000 71400 246580 170000 76600 2 374 120000 90600 201000 191000 138000 3 374 130000 78560 . 155500 110000 4 468 55000 47000 95200 68200 40450 5 468 51000 32000 115500 90000 46000 6 468 46000 40500 . 100300 55000 7 157 . . . . . 8 278.96 . . . . . 9 273.21 . . . . . 10 289.47 . . . . . 11 (US290)
98.97 . . . . .
Table C2. Example of ME Log-Transformation of Table B1 Data.
Rows Log Micro Strain
Log Nf Lab
Bryan-0M
Log Nf Lab
Bryan-3M
Log Nf Lab
Yoakum-0M
Log Nf Lab
Yoakum-3M
Log Nf Lab
Yoakum-6M
1 5.92 11.78 11.18 12.42 12.04 11.25 2 5.92 11.70 11.41 12.21 12.16 11.84 3 5.92 11.78 11.27 . 11.95 11.61 4 6.15 10.92 10.76 11.46 11.13 10.61 5 6.15 10.84 10.37 11.66 11.41 10.74 6 6.15 10.74 10.61 . 11.52 10.92 7 5.06 . . . . . 8 5.63 . . . . . 9 5.61 . . . . . 10 5.67 . . . . . 11 (US290)
4.59 . . . . .
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APPENDIX C (CONTINUED): BB LABORATORY TEST DATA
Table C3. Example of ME 95 Percent Prediction Interval Estimates of Log Nf
(Bryan Mixture). Rows Log
Micro Strain
Predicted Log Nf
Bryan-0M (Yhat_B0)
Lower 95%
prediction interval
for Yhat_B0
Upper 95%
prediction interval
for Yhat_B0
Predicted Log Nf
Bryan-3M(Yhat_B3)
Lower 95%
prediction interval
for Yhat_B3
Upper 95%
prediction interval
for Yhat_B3
1 5.92 11.75 11.52 11.98 11.29 10.77 11.802 5.92 11.75 11.52 11.98 11.29 10.77 11.803 5.92 11.75 11.52 11.98 11.29 10.77 11.804 6.15 10.83 10.60 11.06 10.58 10.06 11.105 6.15 10.83 10.60 11.06 10.58 10.06 11.106 6.15 10.83 10.60 11.06 10.58 10.06 11.107 5.06 15.32 14.57 16.06 14.02 12.36 15.698 5.63 12.96 12.59 13.32 12.21 11.39 13.039 5.61 13.04 12.66 13.42 12.28 11.43 13.1210 5.67 12.80 12.46 13.15 12.10 11.32 12.8711 (US290) 4.59 17.21 16.14 18.28 15.48 13.08 17.88
Table C4. Example of ME 95 Percent Prediction Interval Estimates of Log Nf
(Yoakum Mixture). Rows Log
Micro Strain
Predicted Log Nf
Yoakum-0M
(Yhat_Y0)
Lower 95%
prediction interval
for Yhat_Y0
Upper 95%
prediction interval
for Yhat_Y0
Predicted Log Nf
Yoakum-3M
(Yhat_Y3)
Lower 95%
prediction interval
for Yhat_Y3
Upper 95%
prediction interval
for Yhat_Y3
1 5.92 12.31 11.57 13.05 12.05 11.54 12.562 5.92 12.31 11.57 13.05 12.05 11.54 12.563 5.92 12.31 11.57 13.05 12.05 11.54 12.564 6.15 11.56 10.82 12.30 11.35 10.84 11.865 6.15 11.56 10.82 12.30 11.35 10.84 11.866 6.15 11.56 10.82 12.30 11.35 10.84 11.867 5.06 15.23 12.50 17.96 14.77 13.13 16.418 5.63 13.30 12.01 14.58 12.97 12.17 13.779 5.61 13.37 12.03 14.70 13.04 12.20 13.8710 5.67 13.17 11.97 14.38 12.85 12.10 13.61
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APPENDIX D: DYNAMIC MODULUS LABORATORY TEST DATA FOR THE M-E PAVEMENT DESIGN GUIDE
Table D1. Summary of DM Values for
Bryan Mixture: Basic TxDOT Type C Mixture [PG 64-22 + Limestone].
Specimen # BDM0001, AV =6.56 Percent Temperature Dynamic Modulus, psi
oC oF 0.1 Hz 0.5 Hz 1.0 Hz 5.0 Hz 10 Hz 25 Hz -10 14 2,833,936 3,359,219 3,512,016 3,959,646 4,093,719 4,340,675 4.4 40 1,362,920 1,742,570 1,922,417 2,313,526 2,529,980 2,753,048
21.1 70 471,605 680,590 808,919 1,125,797 1,300,089 1,599,810 37.8 100 152,623 247,913 297,864 490,257 622,778 878,987 54.4 130 68,023 92,476 106,168 175,264 230,189 366,307
Specimen # BDM0002, AV =7.50 Percent
Temperature Dynamic Modulus, psi oC oF 0.1 Hz 0.5 Hz 1.0 Hz 5.0 Hz 10 Hz 25 Hz
-10 14 2,120,104 2,497,956 2,645,111 3,008,257 3,159,546 3,359,538 4.4 40 1,109,930 1,483,373 1,657,332 2,085,121 2,303,968 2,614,421
21.1 70 418,492 630,972 753,195 1,080,343 1,276,608 1,604,175 37.8 100 172,696 266,202 311,860 531,505 659,501 948,953 54.4 130 52,025 74,158 84,804 138,163 188,041 283,114
Specimen # BDM0003, AV =6.90 Percent Temperature Dynamic Modulus, psi
oC oF 0.1 Hz 0.5 Hz 1.0 Hz 5.0 Hz 10 Hz 25 Hz -10 14 2,316,644 2,778,531 2,950,198 3,420,947 3,601,258 3,895,873 4.4 40 1,269,660 1,634,343 1,813,320 2,221,456 2,431,326 2,738,008
21.1 70 445,048 655,781 781,057 1,103,070 1,288,348 1,601,993 37.8 100 125,313 193,466 226,085 369,658 478,044 645,244 54.4 130 72,983 95,478 104,862 165,952 215,831 338,576
Binder Content = 4.6 percent by weight of aggregate VMA = 14 percent at maximum density
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APPENDIX D (CONTINUED): DM LABORATORY TEST DATA
Table D2. Summary of DM Values for Yoakum Mixture: Rut Resistant 12.5 mm Superpave Mixture [PG 76-22 + Gravel].
Specimen # YDM0001, AV =6.80 Percent
Temperature Dynamic Modulus, psi oC oF 0.1 Hz 0.5 Hz 1.0 Hz 5.0 Hz 10 Hz 25 Hz
-10 14 1,823,472 2,389,410 2,612,666 3,241,115 3,485,344 3,899,108 4.4 40 1,124,434 1,558,590 1,759,177 2,291,190 2,525,325 2,890,051
21.1 70 269,944 504,934 638,616 1,011,870 1,223,640 1,607,120 37.8 100 71,852 124,239 152,333 283,839 388,353 641,603 54.4 130 32,996 46,862 52,547 95,116 135,030 251,495
Specimen # YDM0002, AV =6.90 Percent
Temperature Dynamic Modulus, psi oC oF 0.1 Hz 0.5 Hz 1.0 Hz 5.0 Hz 10 Hz 25 Hz
-10 14 1,102, 693 1,520,779 1,742,483 2,348,088 2,615,828 2,924,933 4.4 40 1,062,343 1,513,991 1,693,229 2,166,255 2,380,446 2,607,213
21.1 70 294,499 513,564 657,877 1,082,518 1,325,065 1,634,097 37.8 100 72,852 119,526 148,635 281,170 383,001 619,616 54.4 130 50,502 63,033 69,038 133,174 187,041 327,597
Specimen # YDM0003, AV =7.30 Percent
Temperature Dynamic Modulus, psi oC oF 0.1 Hz 0.5 Hz 1.0 Hz 5.0 Hz 10 Hz 25 Hz
-10 14 1,131,831 1,576,792 1,770,302 2,275,236 2,518,580 2,810,991 4.4 40 710,395 1,028,477 1,187,351 1,600,694 1,763,615 2,005,712
21.1 70 177,758 325,262 419,899 695,877 863,178 1,057,511 37.8 100 45,933 71,214 88,633 156,858 216,353 342,956 54.4 130 29,530 38,116 41,060 64,324 84,238 127,865
Binder Content = 5.6 percent by weight of aggregate VMA = 15.9 percent at maximum density
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APPENDIX E: EXAMPLE OF PERCENTAGE CRACKING ANALYSIS FROM THE M-E PAVEMENT DESIGN GUIDE SOFTWARE
Table E1. Example of the M-E Pavement Design Guide Software Analysis
for Bryan Mixture based on a 20-Year Design Life (WW Environment). Pavement Structure
HMAC Specimen Traffic ESALs (Millions)
Percent Cracking in Wheelpath (Output from Software)
BDM0001 2.50 26.80 BDM0002 2.50 38.3 BDM0003 2.50 31.80 BDM0001 5.00 45.60 BDM0002 5.00 59.90
PS1
BDM0003 5.00 51.60 BDM0001 2.50 21.9 BDM0002 2.50 36.80 BDM0003 2.50 28.60 BDM0001 5.00 53.90 BDM0002 5.00 71.50
PS2
BDM0003 5.00 63.20 BDM0001 1.25 29.90 BDM0002 1.25 40.10 BDM0003 1.25 36.60 BDM0001 2.50 61 BDM0002 2.50 70.00 BDM0003 2.50 67.20 BDM0001 5.00 78.10 BDM0002 5.00 89.80
PS3
BDM0003 5.00 87.40 BDM0001 1.25 26.60 BDM0002 1.25 43.80 BDM0003 1.25 32.30 BDM0001 2.50 58 BDM0002 2.50 70.10 BDM0003 2.50 64.30 BDM0001 5.00 85.50 BDM0002 5.00 96.25
PS4
BDM0003 5.00 88.30 BDM0001 2.50 7.85 BDM0002 2.50 13.51 BDM0003 2.50 9.02 BDM0001 5.00 15 BDM0002 5.00 20.40 BDM0003 5.00 18.10 BDM0001 25 55.10 BDM0002 25 70.40
PS5
BDM0003 25 63.89
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APPENDIX E (CONTINUED): EXAMPLE OF PERCENTAGE CRACKING ANALYSIS FROM THE M-E PAVEMENT DESIGN GUIDE SOFTWARE
Table E2. Example of the M-E Pavement Design Guide Software Analysis
for Bryan Mixture based on a 20-Year Design Life (DC Environment).
Pavement Structure
HMAC Specimen Traffic ESALs (Millions)
Percent Cracking in Wheelpath (Output from Software)
BDM0001 2.50 18.40 BDM0002 2.50 31.60 BDM0003 2.50 23.70 BDM0001 5.00 40.00 BDM0002 5.00 53.90
PS2
BDM0003 5.00 49.70 BDM0001 2.50 18.40 BDM0002 2.50 27.90 BDM0003 2.50 32.60 BDM0001 5.00 48.50 BDM0002 5.00 72.10
PS3
BDM0003 5.00 57.6 BDM0001 2.50 30.50 BDM0002 2.50 48.80 BDM0003 2.50 36.50 BDM0001 5.00 62.80 BDM0002 5.00 73.00
PS4
BDM0003 5.00 60.40
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APPENDIX F: ME MIXTURE LAB Nf RESULTS Mixture Lab Nf Prediction: ME Approach = 50 Percent Reduction in Flexural Stiffness
Table F1. Example of ME Lab Nf for Bryan Mixture for Wet-Warm (WW) Environment.
0 Months 3 Months 6 Months
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
Pavement Structure
(PS#) Lab Nf
Lower Upper
Lab Nf
Upper Lower
Lab Nf
Lower Upper
1 4,483,670 2,124,669 9,461,849 1,232,934 232,469 6,539,046 755,762 13,829 31,095,112
2 423,048 293,301 610,190 201,184 88,761 456,001 123,017 19,976 757,585
3 460,826 315,567 672,950 214,843 92,205 500,598 130,707 19,828 861,609
4 363,435 257,421 513,108 179,035 82,856 386,855 110,460 20,190 604,323
5 29,828,466 10,197,087 87,254,077 5,284,069 480,383 58,123,166 2,512,795 9,467 66,694,421
Table F2. Example of ME Lab Nf for Yoakum Mixture for Wet-Warm (WW) Environment.
0 Months 3 Months 6 Months
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
Pavement Structure
(PS#) Lab Nf
Lower Upper
Lab Nf
Upper Lower
Lab Nf
Lower Upper
1 4,105,724 267,604 62,992,098 2,592,589 502,685 13,371,222 2,420,257 208,917 28,038,084
2 595,841 164,629 2,156,527 429,285 192,011 959,764 303,309 91,221 1,008,496
3 639,003 168,256 2,426,800 458,188 199,448 1,052,585 327,014 94,442 1,132,320
4 526,257 158,105 1,751,663 382,383 179,264 815,650 265,371 85,614 822,545
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APPENDIX F (CONTINUED): ME MIXTURE LAB Nf RESULTS Mixture LAB Nf Prediction: ME Approach = 50 Percent Reduction in Flexural Stiffness
Table F3. Example of Variance Estimates for Predicted Log ME Lan Nf (Bryan Mixture, WW Conditions).
Micro Strain Log (Micro Strain)
Var(Log(Log Nf))_Bryan-0M
Var(Log(Lab Nf)))_Bryan-3M
157 5.06 0.272 0.602
278.96 5.63 0.132 0.292
273.21 5.61 0.142 0.302
289.47 5.67 0.122 0.282
98.97 4.59 0.392 0.862
Table F4. Example of Variance Estimates for Predicted Log ME Nf (Yoakum Mixture, WW Conditions).
Micro Strain Log (Micro Strain)
Var(Log(Lab Nf)))_Yaokum-0M
Var(Log(Log Nf)))_Yaokum-3M
Var(Log(Log Nf)))_Yaokum-6M
157 5.06 0.632 0.592 0.882 278.96 5.63 0.302 0.292 0.432 273.21 5.61 0.312 0.302 0.452 289.47 5.67 0.282 0.272 0.412 98.97 4.59 - - -
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APPENDIX G: CMSE MIXTURE LAB Nf RESULTS Mixture Lab Nf Prediction: CMSE Approach = 7.5 mm Crack Growth & Propagation through HMAC
Layer
Table G1. Example of Bryan Mixture for Wet-Warm (WW) Environment.
0 Months 3 Months 6 Months
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
PS#
Lab Nf
Lower Upper
Lab Nf
Upper Lower
Lab Nf
Lower Upper
1 6,310,031 5,891,450 7,896,612 2,419,856 2,175,875 3,181,037 940,447 820,866 1,258,028
2 4,310,723 4,008,142 4,613,304 2,311,781 1,809,200 2,814,362 1,001,560 798,979 1,204,141
3 4,425,803 4,120,250 4,728,412 2,428,810 1,926,329 2,931,491 1,211,403 1,008,822 1,413,984
4 3,960,542 3,955,200 4,005,620 2,189,413 1,686,832 2,691,994 1,309,518 1,106,937 1,512,099
5 11,123,548 9,820,967 13, 118,456 8,600,514 7,397,933 9,803,095 5,081,720 4,279,139 5,884,301
Table G2. Example of Yoakum Mixture for Wet-Warm (WW) Environment.
0 Months 3 Months 6 Months
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
PS#
Lab Nf
Lower Upper
Lab Nf
Upper Lower
Lab Nf
Lower Upper
1 7,879,929 6,315,948 8,921,110 4,954,378 3,733,797 5,334,959 3,229,895 2,179,244 3,980,406
2 5,893,480 4,590,899 7,196,061 3,057,842 2,257,261 3,858,423 2,115,169 1,214,568 3,015,750
3 5,899,598 4,597,017 7,202,179 3,118,460 2,317,879 3,919,041 2,009,481 1,108,900 2,910,062
4 4,001,831 3,979,250 4,041,412 3,057,181 2,156,600 3,957,762 1,980,815 1,080,234 2,881,396
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APPENDIX H: CM MIXTURE LAB Nf RESULTS
Mixture Lab Nf Prediction: CM Approach = 7.5 mm Crack Growth & Propagation through HMAC Layer
Table H1. Example of Bryan Mixture for Wet-Warm (WW) Environment.
0 Months 3 Months 6 Months
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
PS#
Lab Nf
Lower Upper
Lab Nf
Upper Lower
Lab Nf
Lower Upper
1 6,290,861 5,825,280 7,626,442 2,313,584 1,651,003 3,452,165 914 ,861 612,480 1,413,442
2 4,811,422 3,910,841 5,712,003 2,011,781 2,011,781 2,912,362 989,795 589,214 1,390,376
3 4,181,312 3,980,731 4,381,893 2,611,912 2,611,912 3,512,493 1,009,215 808,634 1,209,796
4 3,980,182 3,959,601 4,000,763 2,204,315 2,204,315 3,104,896 995,850 895,264 1,096,431
5 10,891,433 9,690,852 12,092,014 8,401,515 8,401,515 9,902,096 4,890,253 3,889,672 5,890,834
Table H2. Example of Yoakum Mixture for Wet-Warm (WW) Environment.
0 Months 3 Months 6 Months
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
95% Lab Nf Prediction Interval
PS#
Lab Nf
Lower Upper
Lab Nf
Upper Lower
Lab Nf
Lower Upper
1 7,281,594 6,121,013 7,922,175 5,169,851 3,960,670 5,761,832 3,132,561 2,633,980 3,335,142
2 4,989,845 4,089,264 5,890,420 3,000,221 2,699,640 3,300,802 2,542,506 2,161,925 2,923,087
3 5,600,125 5,0995,544 6,100,706 2,986,420 2,689,839 3,287,001 1,998,652 1,718,071 2,279,233
4 4,121,458 4,000,877 4,224,039 3,116,108 2,765,527 3,466,689 1,500,824 1,260,243 1,741,405
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APPENDIX I: MIXTURE FIELD Nf RESULTS
ME Approach = 50 Percent Reduction in Flexural Stiffness
Table I1. Example of ME Field Nf (Field Nf = SF × Lab Nf): Bryan Mixture, WW Environment.
0 Months 3 Months 6 Months
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
Pavement Structure
(PS#) Field Nf
Lower Upper
Field Nf
Upper Lower
Field Nf
Lower Upper
1 8.519E+07 4.037E+07 1.798E+08 2.343E+07 4.417E+06 1.242E+08 1.436E+07 2.628E+05 5.908E+08
2 8.038E+06 5.573E+06 1.159E+07 3.822E+06 1.686E+06 8.664E+06 2.337E+06 3.795E+05 1.439E+07
3 8.756E+06 5.996E+06 1.279E+07 4.082E+06 1.752E+06 9.511E+06 2.483E+06 3.767E+05 1.637E+07
4 6.905E+06 4.891E+06 9.749E+06 3.402E+06 1.574E+06 7.350E+06 2.099E+06 3.836E+05 1.148E+07
5 5.667E+08 1.937E+08 1.658E+09 1.004E+08 9.127E+06 1.104E+09 4.774E+07 1.799E+05 1.267E+09
Table I2. Example of ME Field Nf (Field Nf = SF × Lab Nf): Yoakum Mixture, WW Environment.
0 Months 3 Months 6 Months
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
Pavement Structure
(PS#) Field Nf
Lower Upper
Field Nf
Upper Lower
Field Nf
Lower Upper
1 7.801E+07 5.084E+06 1.197E+09 4.926E+07 9.551E+06 2.541E+08 4.598E+07 3.969E+06 5.327E+08
2 1.132E+07 3.128E+06 4.097E+07 8.156E+06 3.648E+06 1.824E+07 5.763E+06 1.733E+06 1.916E+07
3 1.214E+07 3.197E+06 4.611E+07 8.706E+06 3.790E+06 2.000E+07 6.213E+06 1.794E+06 2.151E+07
4 9.999E+06 3.004E+06 3.328E+07 7.265E+06 3.406E+06 1.550E+07 5.042E+06 1.627E+06 1.563E+07
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APPENDIX I (CONTINUED): MIXTURE FIELD Nf RESULTS
CMSE Approach = 7.5 mm Crack Growth and Propagation through HMAC Layer
Table I3. Example of CMSE Field Nf (Field Nf = [SFa × SFh] × Lab Nf): Bryan Mixture, WW Environment.
0 Months 3 Months 6 Months
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
Pavement Structure
(PS#) Field Nf
Lower Upper
Field Nf
Upper Lower
Field Nf
Lower Upper
1 6.922E+07 6.463E+07 8.663E+07 1.893E+07 1.702E+07 2.488E+07 6.034E+06 5.267E+06 8.072E+06
2 4.729E+07 4.397E+07 5.061E+07 1.808E+07 1.415E+07 2.201E+07 6.426E+06 5.126E+06 7.726E+06
3 4.855E+07 4.520E+07 5.187E+07 1.900E+07 1.507E+07 2.293E+07 7.773E+06 6.473E+06 9.073E+06
4 4.345E+07 4.339E+07 4.394E+07 1.712E+07 1.319E+07 2.105E+07 8.402E+06 7.102E+06 9.702E+06
5 1.220E+08 1.077E+08 1.439E+08 6.726E+07 5.786E+07 7.667E+07 3.261E+07 2.746E+07 3.776E+07
Table I4. Example of CMSE Field Nf (Field Nf = [SFa × SFh] × Lab Nf): Yoakum Mixture, WW Environment.
0 Months 3 Months 6 Months
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
Pavement Structure
(PS#) Field Nf
Lower Upper
Field Nf
Upper Lower
Field Nf
Lower Upper
1 1.201E+08 9.629E+07 1.360E+08 4.905E+07 3.697E+07 5.282E+07 2.953E+07 1.993E+07 3.640E+07
2 8.985E+07 6.999E+07 1.097E+08 3.028E+07 2.235E+07 3.820E+07 1.934E+07 1.111E+07 2.758E+07
3 8.995E+07 7.009E+07 1.098E+08 3.088E+07 2.295E+07 3.880E+07 1.837E+07 1.014E+07 2.661E+07
4 6.101E+07 6.067E+07 6.162E+07 3.027E+07 2.135E+07 3.919E+07 1.811E+07 9.878E+06 2.635E+07
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APPENDIX I (CONTINUED): MIXTURE FIELD Nf RESULTS
CM Approach = 7.5 mm Crack Growth and Propagation through HMAC Layer
Table I5. Example of CM Field Nf (Field Nf = [SFa × SFh] × Lab Nf): Bryan Mixture, WW Environment.
0 Months 3 Months 6 Months
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
Pavement Structure
(PS#) Field Nf
Lower Upper
Field Nf
Upper Lower
Field Nf
Lower Upper
1 6.901E+07 6.390E+07 8.366E+07 1.809E+07 1.291E+07 2.700E+07 5.870E+06 3.930E+06 9.069E+06
2 5.278E+07 4.290E+07 6.266E+07 1.573E+07 1.573E+07 2.278E+07 6.351E+06 3.781E+06 8.921E+06
3 4.587E+07 4.367E+07 4.807E+07 2.043E+07 2.043E+07 2.747E+07 6.475E+06 5.188E+06 7.762E+06
4 4.366E+07 4.344E+07 4.389E+07 1.724E+07 1.724E+07 2.428E+07 6.390E+06 5.744E+06 7.035E+06
5 1.195E+08 1.063E+08 1.326E+08 6.571E+07 6.571E+07 7.744E+07 3.138E+07 2.496E+07 3.780E+07
Table I6. Example of CM Field Nf (Field Nf = [SFa × SFh] × Lab Nf): Yoakum Mixture, WW Environment.
0 Months 3 Months 6 Months
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
Pavement Structure
(PS#) Field Nf
Lower Upper
Field Nf
Upper Lower
Field Nf
Lower Upper
1 1.110E+08 9.332E+07 1.208E+08 5.119E+07 3.921E+07 5.705E+07 2.864E+07 2.409E+07 3.050E+07
2 7.608E+07 6.234E+07 8.981E+07 2.970E+07 2.673E+07 3.268E+07 2.325E+07 1.977E+07 2.673E+07
3 8.538E+07 7.775E+08 9.301E+07 2.957E+07 2.663E+07 3.254E+07 1.828E+07 1.571E+07 2.084E+07
4 6.284E+07 6.100E+07 6.440E+07 3.085E+07 2.738E+07 3.432E+07 1.372E+07 1.152E+07 1.592E+07
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APPENDIX I (CONTINUED): MIXTURE FIELD Nf RESULTS
The M-E Pavement Design Guide = 50 Percent Cracking in Wheelpath
Table I7. Example of 0 Months Results with Global Aging Model Analysis based on a 20-Year Design Life (WW Environment).
Bryan Mixture Yoakum Mixture
95% Field Nf Prediction Interval
95% Field Nf Prediction Interval
PS#
Field Nf
Lower Upper
Field Nf Lower
Lower Upper
1 4.705E+06 1.927E+06 9.737E+06 6.210E+06 2.037E+06 1.534E+07
2 4.047E+06 1.996E+06 6.354E+06 5.750E+06 2.348E+06 1.054E+07
3 1.932E+06 0.000E+00 3.737E+06 3.410E+06 1.345E+05 7.771E+06
4 2.018E+06 2.802E+05 3.563E+06 2.970E+06 3.491E+05 6.000E+06
5 1.929E+07 1.420E+07 2.483E+07 - - -
Table I8. Example of 0 Months Results with Global Aging Model Analysis based on a 20-Year Design Life
(DC Environment). Bryan Mixture
95% Field Nf Prediction Interval
PS#
Field Nf Lower Upper
2 5.229E+06 2.948E+06 9.924E+06
3 4.290E+06 1.646E+06 7.836E+06
4 3.563E+06 2.639E+05 6.530E+06
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APPENDIX I (CONTINUED): MIXTURE FIELD Nf RESULTS
Example of CMSE and CM Field Nf Prediction at Year 20 (PS# 1, WW Environment)
Table I9. Example of CMSE Field Nf Prediction at Year 20 (PS# 1, WW Environment)
HMAC Mixture SFag @ SFa SFh [Ni + Np] Nf = [SFag ]× [SFa × SFh] ×[Ni + Np]
Bryan 0.045 1.63 6.73 6.31E+06 3.11E+06 Yoakum 0.070 2.10 7.26 7.88E+06 8.40E+06
Table I10. Example of CM Field Nf Prediction at Year 20 (PS# 1, WW Environment)
HMAC Mixture SFag @ SFa SFh [Ni + Np] Nf = [SFag ]× [SFa × SFh] ×[Ni + Np]
Bryan 0.045 1.63 6.73 6.29E+06 3.10E+06 Yoakum 0.070 2.10 7.26 7.28E+06 7.77E+06
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APPENDIX I (CONTINUED): MIXTURE FIELD Nf RESULTS
Example of ME Field Nf Prediction at Year 20 (PS# 1, WW Environment)
1.0E+05
1.0E+06
1.0E+07
0 5 10 15 20 25
Pavement Age (Years)
Mea
sure
d La
b N
f
Bryan Yoakum
Figure I1. Example of Lab Nf Trend with Pavement Age (0 months ≅ 0 years, 3 months ≅ 6 years, and 6 months ≅12 years).
Approximate Lab Nf values at year 20 based on extrapolations in Figure I1 are approximately:
Bryan mixture: Lab Nf = 0.20 E+06
Yoakum mixture: Lab Nf = 1.56 E+06
Using the following ME equation (Chapter 4) with SF = 19, M = 3.57, and TCF = 1, the field Nf
values at year 20 are approximately predicted as follows:
( )[ ]TCFM
NLabSFTCFM
kSFFieldN f
kti
f ×
×=
×=
− 2ε
Bryan mixture: Field Nf ≅ 19* 0.20E+06/(3.57*1) ≅ 1.03 E+06
Yoakum mixture: Field Nf ≅19*1.56E+06/(3.57*1) ≅ 8.30 E+06
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APPENDIX J: RESOURCE REQUIREMENTS
Table J1. Approximate Time (hrs) Requirement to Produce at Least One Mixture Nf Result.
Task 2002 Guide ME CMSE CM
Specimen fabrication 43.75 hrs 45.5 hrs 43.75 hrs 43.75 hrs
Specimen temperature conditioning 20 hrs 4 hrs 15 hrs 11 hrs Lab testing (including set-up) 5 hrs 30 hrs 70 hrs 5 hrs Data analysis 4.5 hrs 3 hrs 6 hrs 5 hrs
Total 72.25 hrs 82.5 hrs 134.75 hrs 64.75 hrs
Note: For the CMSE approach, about 65 hrs lab testing is for surface energy measurements. SE values for asphalts and aggregates are required as CMSE input. Though the current SE test protocol for aggregates might require a test time of about 30 to 60 hrs per aggregate, various alternate and time efficient SE measurement methods are being investigated in other ongoing research projects. Despite the lengthy test time, SE measurements are only performed once for any asphalt or aggregate type from a particular source (as long as there are no major compositional changes). The SE data can then be utilized for numerous analysis applications including fatigue, permanent deformation, and moisture sensitivity modeling in HMAC pavements. Thus, SE measurements are actually efficient considering their repeated and widespread use for asphalt and aggregate materials that may be utilized in different mixture designs.
Table J2. Typical Equipment Requirements.
Task 2002 Guide ME CMSE CM
Binder-Aggregate Mixing Electric mixer Electric mixer Electric mixer Electric mixer
Compacting SGC Linear kneading SGC SGC
Testing MTS LVDTs Control unit
MTS LVDT Control unit BB device
MTS LVDTs Control unit Whilmey Plate USD device
MTS LVDTs Control unit
Data acquisition Automated computer system
Automated computer system
Automated computer system
Automated computer system
Temperature control unit Thermocouples Thermocouples Thermocouples Thermocouples
Other test accessories Attachment plates Attachment plates
Data analysis 2002 Software Excel/manual Excel/manual Excel/manual
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APPENDIX J (CONTINUED): RESOURCE REQUIREMENTS
Table J3. Approximate Time (hrs) Requirements for a Single Specimen Fabrication.
# Task ME
(Beam Specimen) CMSE, CM, & M-E Pavement
Design Guide (Cylindrical Specimen)
1 Aggregate batching 0.5 hrs 0.5 hrs
2 Aggregate pre-heating (minimum ≅ 4 hrs)
12 hrs (overnight)
12 hrs (overnight)
3 Binder liquefying (heating) 0.5 hrs 0.5 hrs
4 Binder aggregate mixing 0.25 hrs 0.25 hrs
5 PP2 Short-Term Oven Aging @ 135 °C (275 °F) 4 hrs 4 hrs
6 Heating for compaction 0.5 hrs 0.5 hrs 7
Compaction 0.25 0.25 hrs
8 Specimen cooling 12 hrs (overnight)
12 hrs (overnight)
9 Sawing & coring (with water) 2 hrs 0.5 hrs
10 Drying after sawing/coring 12 hrs (overnight)
12 hrs (overnight)
11 AV measurements 0.75 hrs 0.25 hrs 12 Cleaning up 1 hrs 1 hrs Total 45.75 hrs 43.75 hrs
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APPENDIX K: TxDOT EVALUATION SURVEY QUESTIONNAIRE
Evaluation & Weighting of Factors for the Selection of Appropriate Fatigue Analysis Approach.
Factor Rating: 1-10
(1 = least important) (10 = most important)
Sub-factor Rating: 1 – 10 (1 = least important) (10 = most important)
Simplicity Equipment availability Equipment versatility
Laboratory testing
Human resources Traffic Materials
Input variability
Environment (temperature & moisture)
Mixture volumetrics Modulus/stiffness Tensile strength Aging Healing Fracture
Incorporation of material properties in analysis
Anisotropy Simplicity Versatility of inputs
Analysis
Definition of failure criteria Nf variability Results Tie to field validation Lab testing (hrs) Equipment ($) Analysis (hrs) -Lab data reduction -Nf computation
Cost
Practicality of implementation
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APPENDIX L: RATING CRITERIA OF THE FATIGUE ANALYSIS APPROACHES
ME CMSE CM 2002 GUIDE CATEGORY WEIGHT (1)
ITEM WEIGHT(2) SCORE EVALUATION SCORE EVALUATION SCORE EVALUATION SCORE EVALUATION
COMMENT
Nf variability 50% 3/10 3.30% 8/10 8.80% 7/10 7.70% 5/10 5.50%Tie to field validation 50% 5/10 5.50% 5/10 5.50% 5/10 5.50% 5/10 5.50%
Results 22%
100% 40% 9% 65% 14% 60% 13 50% 11% CMSE
Practicality 32% 6/10 3.46% 6/10 3.5% 6/10 3.5% 6/10 3.5%
Testing (hrs) 32% 4/10 2.30% 7/10 4% 8/10 4.6% 7/10 4%Analysis (hrs) 19% 8/10 2.74% 6/10 2.05% 6/10 2.05% 6/10 2.05%
Equipment ($) 17% 6/10 1.84% 8.5/10 2.6% 8/10 2.45% 8/10 2.45%
Cost 18%
100% 57% 10% 65% 12% 70% 13% 67% 12%
CM
Materials 36% 5/10 3% 8/10 5% 8/10 5% 6/10 3%Traffic 34% 5/10 3% 5/10 3% 5/10 3% 9/10 5%
Environment 29% 5/10 2% 5/10 2% 5/10 2% 8/10 4%
Input variability
16%
100% 50% 8% 60% 10% 60% 10% 75% 12%
2002 GUIDE
Failure criteria 41% 5/10 3% 8/10 5% 7/10 4% 5/10 3.1%Simplicity 36% 8.5/10 5% 5/10 3% 6/10 3% 6/10 3.2%Versatility of inputs 23% 4/10 1% 10 3% 8/10 3% 7/10 2.4%
Analysis 15%
100% 60% 9% 74% 11% 69% 10% 58% 9%
CMSE
Simplicity 32% 5/10 2.4% 8/10 3.84% 9/10 4.3% 9/10 4.32%
Equipment availability 29% 3/10 1.3% 7/10 3.05% 7/10 3.0% 7/10 3.05%Equipment versatility 22% 2/10 0.7% 10/10 3.30% 8/10 2.3% 8/10 2.64%Human resources 18% 5/10 1.4% 8/10 2.16% 8/10 2.2% 8/10 2.16%
Lab testing 15%
100% 38% 6% 82% 12% 81% 12% 81% 12%
CMSE
Mixture volumetrics 17% 6/10 1.4% 9/10 2.1% 9/10 2.1% 10/10 2.4%Modulus/stiffness 17% 8/10 1.9% 9/10 2.1% 9/10 2.1% 10/10 2.4%
Fracture 16% 5/10 1.1% 10/10 2.2% 8/10 1.8% 5/10 1.1%
Tensile strength 15% 5/10 1.1% 10/10 2.1% 1/100 2.1% 5/10 1.1%
Aging 14% 5/10 1.0% 9/10 1.8% 9/10 1.8% 8.5/10 1.8%Healing 12% 5/10 0.8% 9/10 1.5% 7.5/10 1.3% 5/10 0.8%
Anisotropy 9% 5/10 0.6% 9/10 1.1% 9/10 1.1% 5/10 0.6%
Incorporation of Material Properties
14%
100% 57% 8% 93% 13% 88% 12% 73% 10%
CMSE
Total 100% 50% 72% 70% 66% CMSE Example of Score and Evaluation Calculations: Evaluation = [Score × Weight (1) × Weight (2)], Score sub-total = ∑[Score ×Weight (2)], and Total scores = ∑[Evaluation]
